Acceleration
A cart gains speed on a straight lane. How quickly is its velocity changing?
Drag the time and watch the velocity arrow. Then tap the braking bus.
Loading lab…
- At t = 0 s the cart's velocity is 4 m/s.
- At t = 3 s it is 8.5 m/s.
- At t = 6 s it is 13 m/s.
- It gains 1.5 m/s every second.
The cart's velocity changes by 1.5 m/s in every second.
The rule
Acceleration is the change in velocity divided by the time taken. Its unit is metre per second squared.
The formula is a = (v − u) ÷ t. Here a is acceleration and t is the time taken. The letter u is the first velocity and v the last. For the cart, a = (13 − 4) ÷ 6 = 9 ÷ 6 = 1.5 m/s².
If the acceleration points against the velocity, the object slows down. Motion to the right and a negative acceleration mean slowing down. A bus brakes from 20 m/s to rest in 4 s. At rest, v = 0. So a = (0 − 20) ÷ 4 = −5 m/s².
Air drag is air pushing against a moving object. Ignore air drag. Near Earth, a falling stone gains 9.8 m/s each second. Its acceleration is 9.8 m/s².
A bend also gives acceleration, because the direction of the velocity changes.
Watch out!
A fast object can have zero acceleration. Acceleration is how quickly velocity changes, not how big the velocity is.