MOTION

DISTANCE.

Distance is the measure of the amount of how far a body has moved between two points. Distance is a scalar quantity and the SI unit is meter (m).

DISPLACEMENT.

Displacement is the total distance covered in a specified direction. It is the measure of the shortest distance a body traveled as a result of change in position. It is a vector quantity and the SI unit is meter (m).

SPEED.

Speed is the rate of change of distance per unit time. That is, how fast a body is moving.

                                                  speed = distance/time

                                                             s = d/t

It is a scalar quantity and the SI unit is m/s

VELOCITY.

Velocity is the rate of change of displacement with time. That is how far a body is moving in a specified direction.

                                                   velocity = displacement/time

                                                      v = d/t

 It is a vector quantity and the SI unit is m/s.

ACCELERATION. 

Acceleration is the rate of change of velocity with time.

                                acceleration = velocity/time = final velocity - initial velocity/ time 

 It is a vector quantity and the SI unit is m/s²

EXAMPLE 1:

Khalid walks a distance of 12.8 m in 21 s. Calculate Khalid’s speed.

SOLUTION:

Given                                                                          Unknown

distance = 12.8 m                                                       speed = ?

time = 21 s

                       s = d/t = 12.8 m / 21 s = 0.6 m/s

EXAMPLE 2:

Calculate the velocity of a car that has covered a displacement of 5 Km in Northeast direction in 36 s.

SOLUTION:

Given                                                                          Unknown

Displacement = 5 Km = 5000 m                                             velocity = ?

Time = 36 s

                                                 velocity = displacement / time

                                                   v = 5000 m / 36 = 138.8 m/s

EXAMPLE 3:

The principal’s car moves with a velocity of 25 m/s and changes to a velocity of 32 m/s in 6 s. Find the acceleration of the car.

SOLUTION:

Given                                                                          Unknown

Initial velocity (u) = 25 m/s                                        acceleration = ?

Final velocity (v) = 32 m/s

Time = 6 s

                                            acceleration = final velocity - initial velocity / time 

                                                        a = v - u / t = 32 m/s - 25 m/s / 6 s = 1.17 m/s²

EXAMPLE 4:

A young girl drops a ball from a balcony. The ball strikes the ground in 4.5 seconds. What is the velocity of the ball the instant before it hits the ground?

SOLUTION:

Given                                                                          Unknown

Time = 4.5 s                                                                v = ?

Note: Since the ball is falling towards the ground, the acceleration will be due to gravity which is 9.8 m/s².

                                                    acceleration = velocity / time 

                                                    velocity = acceleration × time = 9.8 m/s² × 4.5 s = 44.1 m/s