Linear motion, equations of motion (A-level physics)

Linear motion

Terms used

Displacement is the distance moved by a body in a specific direction

Velocity is the rate of change of displacement

Uniform velocity is the constant rate of change of displacement

Acceleration is the rate of change of velocity.

Displacement time graphs

Velocity time graph

Note: when velocity  is uniform/constant or maximum, acceleration is zero

          When the body starts from rest, initial velocity, u=0

          When a body comes to the rest, the final velocity, v = 0

Equations of motion

Usual symbols

u – initial velocity

v- final velocity

s – displacement

a – acceleration

t – time

If a body’s velocity changes from u to v in time t, then

Example 1

A motorist travelling at constant speed of 50kmh^-1 passes a motor cyclist starting of in the same direction. If the motorist maintains a constant acceleration of 2.8m/s²,

(a) Calculate  the time taken by the motorist to catch up with the motorist.

Motorist

Examples 2

A motor car moving with uniform acceleration covers 5.5m in the 4^th second and 9.5m in the 8^th second in its motion. Find its acceleration and the initial velocity.

Solution

From s = ut + ½ at²

Distance covered in 4^th second = (distance covered in first 4seconds

                                                         – distance covered in first 3 second)

                                          5.5  = (4u + ½ a x 4²) – (3ut + ½ a x 4²)

                                           11 = 2u + 7a ……………………….. (a)           

Distance covered in 8^th second = (distance covered in first 4seconds

                                                         – distance covered in first 3 second)

                                          9.5  = (8u + ½ a x 8²) – (7ut + ½ a x 7²)

                                           19 = 2u + 15a ……………………….. (b)

Solving: a = 1ms^-2; u = 2ms^-1