Acceleration as change in velocity per second, deceleration, and what the gradient and the area of a velocity-time graph give you.
What you will learn
- Calculate acceleration with a = Δv ÷ t
- Find acceleration from the gradient of a velocity-time graph
- Find distance from the area under it
Acceleration is change per second
Acceleration is how much the velocity changes every second.
acceleration = change in velocity ÷ time taken
a = (v − u) ÷ t
u is the starting velocity, v the final one. The unit is m/s² ("metres per second, per second"): an acceleration of 3 m/s² adds 3 m/s to the velocity every second.
Slowing down gives a negative acceleration. Questions often call it a deceleration and want the positive number: a car going from 20 m/s to rest in 4 s has a = −5 m/s², a deceleration of 5 m/s².
To find a final velocity: change in velocity = acceleration × time, then add it to the starting velocity (u = 0 if it starts from rest). A bus at 4 m/s accelerating at 1.5 m/s² for 6 s gains 9 m/s, so v = 13 m/s.
Typical accelerations are worth knowing for estimates: an object falling freely near the Earth, about 10 m/s² (9.8 m/s²); a car pulling away gently, about 2 m/s².
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Acceleration is change per second
- Velocity-time graphs
- Try it: Push the block and watch the graph
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Deceleration, Gradient, Constant velocity, Area under the line
In this unit: Forces and motion
Speed, velocity and acceleration, the graphs that show them, the equations of motion, Newton's laws and stopping distances.