v = u + at
Final velocity from initial velocity, acceleration and time.
Predicting the speedometer
A bus is moving at some velocity and speeds up steadily. You know its acceleration and for how long it speeds up.
How could you find its final velocity?
What this lesson covers
The idea
For constant acceleration, v = u + at, where u is the initial velocity, v the final velocity after time t, and a the acceleration.
Predicting the speedometer
A bus is moving at some velocity and speeds up steadily. You know its acceleration and for how long it speeds up.
How could you find its final velocity?
- Add the gain in velocity to the starting velocity
- Multiply the starting velocity by the time
- Subtract the time from the starting velocity
Build the final velocity
Set the values from the bus examples and read the final velocity.
The gain in velocity
In each second the velocity gains a (the acceleration). In t seconds it gains at. So the final velocity is the starting velocity plus the gain: 10 + 0.5 × 10 = 15 m s⁻¹. For the braking bus the gain was −15, so 15 − 15 = 0.
For constant acceleration, v = u + at, where u is the initial velocity, v the final velocity after time t, and a the acceleration. It follows from a = (v − u)/t.
Notes
For constant acceleration, v = u + at: final velocity = initial velocity + acceleration × time.
Check yourself
A bus has an initial velocity of 10 m s⁻¹ and a constant acceleration of 0.5 m s⁻². What is its velocity after 10 s?
Answer: 15 m s⁻¹
v = 10 + 0.5 × 10 = 15 m s⁻¹.
A car starts from rest (u = 0) with a constant acceleration of 2 m s⁻². What is its velocity after 5 s?
Answer: 10 m s⁻¹
v = 0 + 2 × 5 = 10 m s⁻¹.
A bus moving at 15 m s⁻¹ has a constant acceleration of −3 m s⁻². What is its velocity after 5 s?
Answer: 0 m s⁻¹
v = 15 + (−3) × 5 = 0 m s⁻¹.
In v = u + at, what does u stand for?
- The final velocity. The final velocity is v.
- The initial velocity — correct. Yes!
- The time. The time is t. The letter u stands for the initial velocity.