Acceleration
When an object changes velocity, it accelerates. The rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity ÷ time taken. is the change in velocity per second and is measured in m/s2.
The relationship between acceleration, velocity change and the time taken for the change is given by this formula.
\(\text{acceleration}=\frac{\text{change in velocity}}{\text{time taken}}=\frac{\text{v - u}}{\text{t}}\)
v = final velocity and u = starting velocity.
Question
Find the acceleration of a car, if it starts at 10 m/s and it reaches 30 m/s in 4 seconds.
The change in velocity is v – u, which is 30 – 10 = 20 m/s.
The acceleration is the change in velocity ÷ time, which is 20 m/s ÷ 4 s = 5 m/s2.
Question
What happens if the car slows down? Can you work out the acceleration now?
Find the acceleration of the car, if it starts at 20 m/s and it reaches 12 m/s in 2 seconds.
The change in velocity is v – u, which is 12 – 20 = -8 m/s.
The acceleration is the change in velocity ÷ time, which is -8 m/s ÷ 2 s = -4 m/s2.
A minus sign means that the car is decelerating.
Question
A car can accelerate from 22 m/s (50 mph) to 30 m/s (70 mph) in 4 seconds. Calculate the acceleration.
The change in velocity v – u = 30 – 22 = 8 m/s.
The acceleration = change in velocity ÷ time = 8 m/s ÷ 4 s = 2 m/s2.
Question
A motorcycle goes from 0 m/s (rest) to 40 m/s in 8 seconds. Calculate the acceleration.
The change in velocity v – u = 40 – 0 = 40 m/s.
The acceleration = change in velocity ÷ time = 40 m/s ÷ 8 s = 5 m/s2.
Question
A sports car can accelerate from 0 to 26 m/s (60 mph) in 5 seconds. What is the acceleration of the car?
The change in velocity v – u = 26 – 0 = 26 m/s.
The acceleration = change in velocity ÷ time = 26 m/s ÷ 5 s = 5.2 m/s2.
Question
A cyclist brakes and slows from 11 m/s to 3 m/s in 2 seconds. Calculate the acceleration of the bike.
The change in velocity v – u = 3 – 11 = -8 m/s.
The acceleration = change in velocity ÷ time = -8 m/s ÷ 2 s = -4 m/s2.