### Motion-Time Graphs

In this tutorial, **distance-time**, **velocity-time** and **acceleration-time**graphs are explained with the aid of animations.

#### Velocity

The rate of change of displacement - distance in a certain direction - is called the velocity.

Velocity = displacement /time

The **gradient** of a distance time graph is **speed.**

*Units: ms ^{-1}*

#### Acceleration / Deceleration

The rate of change of velocity - speed in a certain direction - is called the acceleration or deceleration.

Acceleration = velocity / time

The **gradient** of a velocity time graph is **acceleration or deceleration.**

*Units: ms ^{-2}*

The following animation help you distinguish between *displacement* and *distance.*

The following animations show displacement / time graphs and their corresponding velocity / time graphs and acceleration / time graphs.

In the animations, please focus on the gradients of displacement-time graphs and velocity-time graphs, that will help understand the relationships.

#### Equations of Motion

From the graph, a = v-u/t => v = u + at 1

From the graph, the area, s = ut + 1/2 (v-u)t => s = ut + 1/2 at^{2} 2

From 1 => v^{2 = u2} + 2uat + a^{2}t^{2}

v^{2} = u^{2} + 2a(ut + 1/2 at^{2})

v^{2} = u^{2} + 2as 3

#### The Motion of a Ball Thrown upwards...

The following animation models a ball thrown upwards until it comes back down and hits the ground.

The velocity of the ball comes down, then becomes instantaneously zero and increases again. The corresponding displacement-time and acceleration-time graphs are shown on the same grid.

Now practise the following to complement what you have learnt so far.

Draw distance-time graphs and corresponding velocity-time graph and acceleration-time graphs for the following:

- A ball dropped from the top of a tower
- A ball dropped from the top of a tower on to a perfectly elastic floor to be bounced back once
- A ball thrown upwards and then catch it again after a while
- The motion of an aircraft on landing after a long journey
- The motion of a parachutist when coming down
- The motion of a feather in the air