How quickly does velocity change?

The idea

Average acceleration = change in velocity ÷ time interval: a = (v – u)/(t2 – t1), where u is the velocity at time t1 and v the velocity at time t2; its SI unit is m s–2.

The jolt in a bus

You sit in a bus. When it suddenly starts you feel a jolt, and when it suddenly stops you feel another.

What do you think these jolts tell us is changing?

• The velocity of the bus
• The colour of the road
• The mass of the bus

Change in velocity

Set the numbers for a bus speeding up and then braking, and read the acceleration.

Per second

When the velocity went from 10 to 15 m s⁻¹ in 10 s, the change of 5 m s⁻¹ over 10 s gave 0.5 m s⁻², which is the velocity change per second. When the bus braked from 15 m s⁻¹ to 0 in 5 s, the change was −15 m s⁻¹ and the average acceleration −3 m s⁻².

Average acceleration = change in velocity ÷ time interval: a = (v − u)/(t2 − t1), where u is the velocity at time t1 and v the velocity at time t2. Its SI unit is m s⁻².

Notes

Average acceleration a = (v − u) ÷ (t2 − t1) = change in velocity ÷ time interval. Unit m s⁻².

Check yourself

A bus changes its velocity from 10 m s⁻¹ to 15 m s⁻¹ in 10 s. What is its average acceleration?

Answer: 0.5 m s⁻²

a = (15 − 10) m s⁻¹ ÷ 10 s = 0.5 m s⁻².

A bus slows from 15 m s⁻¹ to rest in 5 s. What is its average acceleration?

Answer: -3 m s⁻²

a = (0 − 15) m s⁻¹ ÷ 5 s = −3 m s⁻².

What is the SI unit of average acceleration?

In a = (v − u)/(t2 − t1), what does u stand for?

• m s⁻¹. m s⁻¹ is the unit of velocity. Acceleration is a change of velocity per second.
• m. The metre is the unit of distance and displacement.
• m s⁻² — correct. Yes!
• The velocity at time t1 — correct. Yes!
• The velocity at time t2. The velocity at time t2 is v.
• The time interval. The time interval is t2 − t1. The letter u stands for the initial velocity.