2.1 – Motion

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

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.  $120 \mathrm{m}$

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 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.

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.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

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

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.

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

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.  $\frac{1}{2}gt\left(T-t\right)$

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

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.

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.

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.

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?

Comment on the magnitude of the force in (b)(ii).

Comment on the magnitude of the force in (b)(ii).

Comment on the magnitude of the force in (b)(ii).

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.  $\frac{u \sin \theta }{g}$

Show that the acceleration of the sledge is about –2 m s^–2.

Show that the acceleration of the sledge is about –2 m s^–2.

Show that the acceleration of the sledge is about –2 m s^–2.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Estimate the maximum speed of the spacecraft.

Estimate the maximum speed of the spacecraft.

Estimate the maximum speed of the spacecraft.

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.

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.

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 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 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?

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 $V_{\text{v}}$?

Determine H.

Determine H.

Determine H.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

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 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 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 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

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.