Acceleration and kinematics
Use signed velocity changes and know when constant-acceleration equations apply.
What you will learn
- Calculate average acceleration.
- Interpret a velocity–time graph.
Velocity includes direction
Acceleration is the rate of change of velocity, so it can arise from a change in speed or direction. In one dimension, choose a positive direction and keep the signs of initial and final velocity consistent.
Average acceleration over an interval is (v−u)/t. This does not show every instantaneous acceleration during that interval; uniform acceleration means the instantaneous value stays constant.
Connect equations to graphs
The gradient of a velocity–time graph gives acceleration. Its signed area gives displacement. For constant acceleration, the graph is a straight line and the mean velocity is (u+v)/2.
Equations such as v=u+at and s=ut+1/2at² assume constant acceleration. Check that assumption before using them.
Worked example
A vehicle's velocity changes uniformly from 5 to 17 m/s in 4 s. Find acceleration and displacement.
Show the worked solution
- Acceleration is (17−5)/4=3 m/s².
- Mean velocity is (5+17)/2=11 m/s.
- Displacement is 11×4.
Answer 3 m/s² and 44 m
Common mistakes
- Subtract initial velocity from final velocity, not the reverse.
- Distance and displacement differ when direction changes.
What can you explain now?
Velocity changes from 12 to 3 m/s in 3 s. Find average acceleration.
Compare with the explanation
−3 m/s²
The velocity change is −9 m/s, so acceleration is −9/3. The negative sign is relative to the chosen direction.
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