Motion-Time Graphs

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.
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 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.

moving ball under gravity


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:

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





Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.


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