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.

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- Question
A car can accelerate from 22 m/s to 30 m/s in 4 seconds. Calculate the acceleration of the car.

Final velocity v = 30 m/s.

Initial velocity u = 22 m/s.

The final velocity v – initial velocity u = 30 m/s – 22 m/s

= 8 m/s.

The acceleration = (final velocity v – initial velocity u) ÷ time = 8 m/s ÷ 4 s = 2 m/s

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

^{2}.

- Question
A motorcycle goes from rest (0 m/s) to 40 m/s in 8 seconds. Calculate the acceleration.

Final velocity v = 40 m/s.

Initial velocity u = 0 m/s.

The final velocity v – initial velocity u = 40 m/s – 0 m/s

= 40 m/s.

The acceleration = (final velocity v – initial velocity u) ÷ time = 40 m/s ÷ 8 s = 5 m/s

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

^{2}.

- Question
While riding his bike, Jacob brakes and slows from 11 m/s to 3 m/s in 2 seconds. Calculate Jacob’s acceleration.

Final velocity v = 3 m/s.

Initial velocity u = 11 m/s.

The final velocity v – initial velocity u = 3 m/s – 11 m/s

= -8 m/s.

The acceleration = (final velocity v – initial velocity u) ÷ time = -8 m/s ÷ 2 s = -4 m/s

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

^{2}(or a retardation of 4 m/s^{2}).