A.1 Kinematics

Calculate d.

Calculate d.

Calculate d.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

Ball 1 is dropped from rest from an initial height $h$. At the same instant, ball 2 is launched vertically upwards at an initial velocity $u$.

At what time are both balls at the same distance above the ground?

A.  $\frac{h}{4u}$

B.  $\frac{h}{2u}$

C.  $\frac{h}{u}$

D.  $\frac{2h}{u}$

Ball 1 is dropped from rest from an initial height $h$. At the same instant, ball 2 is launched vertically upwards at an initial velocity $u$.

At what time are both balls at the same distance above the ground?

A.  $\frac{h}{4u}$

B.  $\frac{h}{2u}$

C.  $\frac{h}{u}$

D.  $\frac{2h}{u}$

A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?

A. 0.1 g

B. 0.3 g

C. 0.9 g

D. 3 g

A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?

A. 0.1 g

B. 0.3 g

C. 0.9 g

D. 3 g

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

A projectile is launched at an angle above the horizontal with a horizontal component of velocity $V_{\text{h}}$ and a vertical component of velocity $V_{\text{v}}$. Air resistance is negligible. Which graphs show the variation with time of $V_{\text{h}}$ and of $V_{\text{v}}$?

A projectile is launched at an angle above the horizontal with a horizontal component of velocity $V_{\text{h}}$ and a vertical component of velocity $V_{\text{v}}$. Air resistance is negligible. Which graphs show the variation with time of $V_{\text{h}}$ and of $V_{\text{v}}$?

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

A ball is thrown upwards at time t = 0. The graph shows the variation with time of the height of the ball. The ball returns to the initial height at time T.

What is the height h at time t ?

A.  $\frac{1}{2}g{t}^2$

B.  $\frac{1}{2}g{T}^2$

C.  $\frac{1}{2}gT\left(T-t\right)$

D.  $\frac{1}{2}gt\left(T-t\right)$

A ball is thrown upwards at time t = 0. The graph shows the variation with time of the height of the ball. The ball returns to the initial height at time T.

What is the height h at time t ?

A.  $\frac{1}{2}g{t}^2$

B.  $\frac{1}{2}g{T}^2$

C.  $\frac{1}{2}gT\left(T-t\right)$

D.  $\frac{1}{2}gt\left(T-t\right)$

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.

Estimate the acceleration of the bottle when it is at its maximum height.