Scientists often make measurements. The physical quantities they measure fall into two categories: scalars and vectors. Scalar and vector quantities are treated differently in calculations.

Part of

When an object changes velocity, it accelerates.

Acceleration is the change in velocity per second and is measured in m/s^{2}.

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 =

**v** = final velocity and **u** = initial velocity

If an object has an acceleration of 10 m/s^{2} 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/s

^{2}.The acceleration of the car is 5 m/s

^{2}.

- 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/s

^{2}.The car has an acceleration of -4 m/s

^{2}.A negative acceleration is called a

**retardation**.A

**minus sign**means that the car is slowing down and has a retardation of 4 m/s^{2}.