Kinematics

Kinematics deals with motion of a body without referring to the forces that cause the motion. We study properties such as displacement, distance, speed, velocity and acceleration with time

Distance, s is the measure of separation between two points A B.

Displacement s is the distance moved in a particular direction or the change from its initial position to its final position

For a car that finishes 1 complete lap on a 20 km closed circular loop race track, would have travelled a distance of 20 km, but have a displacement of 0 because it returned to its original position

Speed, v is the rate at which an object changes its distance with time.

Unit: m/s

An object is moving at a constant speed if it moves equal distances in equal successive time interval

Look at the graph of displacement with time. Every 1 hour, the distance moved is the same, 45 miles. Therefore the object is moving at constant speed.

Average speed = total distance / total time

If a body completes journey of 20 km in 4 s, its average speed = 20 000/4 = 5000 m/s or 5 km/s

Velocity, v is the rate of change of displacement with time

Unit: m/s

Velocity is speed in a specified direction

Acceleration, a is the rate of change of velocity with time

Unit: m/s2

Acceleration can be calculated using the following equation

a = [final velocity - initial velocity] / time

a = (v-u)/t

If a body, moving at 4 m/s increases speed to 10 m/s in 5 s calculate Its acceleration.

v = 10 m/s

u = 4 m/s

t = 5s

a = (10 - 4) / 5 = 1.2ms-2

A body has uniform acceleration if the rate of change of velocity remains constant over time.

A body has non-uniform acceleration if the rate of change of velocity changes over time, this is its acceleration changes during motion.

Free Fall

By free fall we mean an object that is under the pull of gravity.

Without any resistance, a paper clip and a boulder in free fall, will hit the ground at the same time.

An object in free fall:

- accelerates downwards at a rate of 10 ms-2

- speed continues to increase until it hits the ground

An object in free fall with air resistance

experiences the downward pull of gravity

experiences an upward resistive force caused by the fluid in which it is falling.

Resultant downward force = F (due to the pull of gravity) - F(resistive)

As the object increases speed, F (resistive) increases

If F (due to the pull of gravity) = F(resistive) then the Resultant downward force = 0 and the object no longer accelerates. It continues to fall at its final speed which is its terminal velocity.