On this page we will consider the gradient of and area under velocity-time graphs and the equations that can be derived from these.
Key Concepts
Acceleration is defined as the rate of change of velocity:
\(a={v-u \over t}\)
The SI derived unit of acceleration is m s-2.
All of the equations of motion require constant acceleration.
If the acceleration is constant, average velocity equals the average of the initial and final values. This leads to a suvat equation:
\(s ={(u + v) \over 2}t\)
The gradient of a velocity-time graph = Δv/Δt, this is the acceleration:
\(a={v-u\over t}\)
Displacement-time graphs
Collectively these equations are referred to as suvat because of the quantities involved:
- s = displacement /m
- u = initial velocity /m s-1
- v = final velocity /m s-1
- a = acceleration /m s-2
- t = time /s
Use quizzes to practise application of theory.
START QUIZ!
A body accelerates from 4 ms-1 to 8 ms-1 in 8 s.
The acceleration is ms-2
a = (v - u)/t = (8 - 4)/8
A body travelling at 10 ms-1 to the right undergoes a constant acceleration for 2 minutes. The final velocity is 50 ms-1 to the left
The acceleration is ms-2
a = (v - u)/t = (-50 - 10)/120 = -60/120
A body travelling to the left with velocity 20 ms-1 is accelerated at 10 ms-2 for 2 s.
The final velocity is ms-1
a = (v - u)/t
v = u + at = -20 + 10x2 = 0 ms-1
The displacement time graph represents a body moving with constant acceleration of 1 ms-2
Initial displacement = m
Initial velocity = ms-1
s0 is the y intercept, u is the gradient of the blue line
The displacement time graph represents a body moving with constant acceleration of 1 ms-2
Initial displacement = m
Initial velocity = ms-1
s0 is the y intercept u is the gradient of the blue line
The displacement time graph represents a body moving with constant acceleration of -1 ms-2
Initial displacement = m
B = ms-1
s0 is the y intercept u is the gradient of the blue line
Here are 4 displacement - time graphs
Determine which graph represents which motion.
| Initial displacement /m | Initial velocity/ms-1 | acceleration /ms-2 | graph |
| 2 | 0 | -0.5 | |
| 2 | 1 | -0.5 | |
| 1 | 2 | 2 | |
| 1 | 2 | 1 |
The graph represents the velocity of a body travelling with constant acceleration.
Considering the motion from 0 to 2s determine the following values:
Displacement = m
Initial velocity = ms-1
Final velocity = ms-1
Acceleration = ms-2
s is the area, u is the intercept, a is the gradient
The graph represents the velocity of a body travelling with constant acceleration.
Considering the motion from 0 to 2s determine the following values:
Displacement = m
Initial velocity = ms-1
Final velocity = ms-1
Acceleration = ms-2
The graph represents the velocity of a body travelling with constant acceleration.
Considering the motion from 0 to 8s determine the following values:
Displacement = m
Initial velocity = ms-1
Final velocity = ms-1
Acceleration = ms-2
How much of Linear acceleration have you understood?
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