You are here
When a vehicle suddenly starts or stops, you feel a jolt — the feeling of velocity changing. How do we measure how quickly velocity changes?
- The average acceleration over a time interval is the change in velocity divided by the time interval: a = Change in velocity Time interval = v - u t 2 - t 1 where the velocity changes from u (at t 1 ) to v (at t 2 ).
- SI unit: m s⁻² (m/s²). It has magnitude and direction.
- If the magnitude of velocity is increasing , acceleration is in the direction of velocity; if decreasing , it is opposite to velocity.
- Average acceleration — the change in the velocity of an object over a time interval divided by that time interval; its SI unit is m s⁻².
- The reading of a vehicle’s speedometer is nearly (but not exactly) the magnitude of the velocity at an instant.
- The direction of the tyres gives the direction of velocity at that instant.
In this Activity, we will use the 0-to-100 km/h time of different cars (looked up online) to calculate and compare their average accelerations.
- The acceleration of a car is often quoted as the time to go from 0 to 100 km h⁻¹. Note this time for a few cars, then compute a . (Note: 100 km h -1 ≈ 27.8 m s -1 .)
| Car type | Time interval during which the speed goes from 0 to 100 km h⁻¹ | Magnitude of average acceleration (m s⁻²) |
|---|---|---|
| Sports car | 5 s | ≈ 5.6 |
| Sedan | 8 s | ≈ 3.5 |
| Hatchback | 12 s | ≈ 2.3 |
A bus at 36 km h⁻¹ speeds up to 54 km h⁻¹ in 10 s, then later brakes from 54 km h⁻¹ to rest in 5 s. Find the average acceleration in each interval.
(i) Accelerator: u = 36 km h -1 = 10 m s -1 , v = 54 km h -1 = 15 m s -1 , t = 10 s.
a = 15 - 10 10 = 5 10 = 0.5 m s -2 (in the direction of velocity, since speed is increasing).
(ii) Brake: u = 15 m s -1 , v = 0 , t = 5 s.
a = 0 - 15 5 = -3 m s -2 . The minus sign shows acceleration is opposite to velocity (speed decreasing).
A dropped object has velocity 9.8, 19.6, 29.4, 39.2 m s⁻¹ at t = 1, 2, 3, 4 s. Find its average acceleration in each one-second interval. Is it constant?
9.8 - 0 1 = 9.8, 19.6 - 9.8 1 = 9.8, 29.4 - 19.6 1 = 9.8, 39.2 - 29.4 1 = 9.8 m s -2
The average acceleration is constant, 9.8 m s⁻² , in the direction of motion. This is the acceleration due to gravity, g .
- An object can move very fast and still have zero acceleration . Acceleration depends on how quickly velocity changes , not on how fast the object is going.
- Average acceleration can come from a change in the magnitude of velocity, its direction, or both. In this chapter we consider only cases where acceleration is constant .
- Just like velocity at an instant, the acceleration at a particular instant is called the instantaneous acceleration .
- As the time interval around an instant becomes very small, the average acceleration approaches a fixed value — the instantaneous acceleration. You will learn more about it in higher grades.
-
A car goes 3 km east and then 4 km west. What is the total distance travelled and what is the displacement?
Show Answer
Total distance travelled = 3 + 4 = 7 km. Displacement = 4 − 3 = 1 km towards the west. -
Can the total distance travelled ever be less than the magnitude of the displacement?
Show Answer
No. The path length can never be shorter than the straight-line change in position, so distance ≥ |displacement| always. -
A body returns to its starting point after 10 s. What is its average velocity?
Show Answer
Displacement = 0, so average velocity = 0 ÷ 10 s = 0 — even though the average speed is not zero. -
What does average acceleration measure?
Show Answer
The change in velocity divided by the time interval in which that change happens; its SI unit is m s⁻².
