Acceleration - Higher

When an object changes velocity, it accelerates.

Acceleration is the change in velocity per second and is measured in m/s2.

Acceleration is a vector quantity because it has size and direction.

The relationship between acceleration, change in velocity and the time taken is given by the equation:

acceleration = \frac{\text{final velocity – initial velocity}}{\text{time taken}}

v = final velocity and u = initial velocity

A formula triangle showing that Acceleration is equal to Change in velocity divided by Time taken.

If an object has an acceleration of 10 m/s2 it means that the velocity of the object changes by 10 m/s every second.

Question

Find the acceleration of a car, if it starts at 10 m/s and it reaches 30 m/s in 4 seconds.

Final velocity v = 30 m/s.

Initial velocity u = 10 m/s.

The final velocity v – initial velocity u is 30 m/s – 10 m/s

= 20 m/s.

The acceleration is (final velocity v – initial velocity u) ÷ time, which is 20 m/s ÷ 4 s = 5 m/s2.

The acceleration of the car is 5 m/s2.

Question

Find the acceleration of the car, if it starts at 20 m/s and slows down to 12 m/s in 2 seconds.

Final velocity v = 12 m/s.

Initial velocity u = 20 m/s.

The final velocity v – initial velocity u is 12 m/s – 20 m/s

= -8 m/s.

The acceleration is the (final velocity v – initial velocity u) ÷ time, which is -8 m/s ÷ 2 s = -4 m/s2.

The car has an acceleration of -4 m/s2.

A negative acceleration is called a retardation.

A minus sign means that the car is slowing down and has a retardation of 4 m/s2.