In this tutorial, distance-time, velocity-time and acceleration-timegraphs are explained with the aid of animations.
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.
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.
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 at2 2
From 1 => v2 = u2 + 2uat + a2t2
v2 = u2 + 2a(ut + 1/2 at2)
v2 = u2 + 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