The Basics of Linear Motion and Displacement and Velocity Time-Graphs

Both speed and velocity tell us how far something is travelling in unit time. As velocity is a vector it must also tell us what direction the object is travelling in.

Speed (m/s) =

distance moved (m) time taken (s)

Velocity (m/s) =

displacement change (m) time taken (s)

Acceleration tells us how rapidly something is changing velocity - for instance, the change in velocity in unit time.Deceleration is the same thing, but has a negative sign as the velocity if decreasing.

Question (easy one!):

These show the motion of an object very clearly and allow you to find position and velocity at any time. Any graph that you see will be a combination of these sections.

Notice that the gradient =

change in D (or ΔD) change in t (or Δt)

= the velocity at any time.

When the velocity is changing, as on the lower two graphs, you can find the velocity at any point by drawing a tangent touching the graph at that point by drawing a tangent touching the graph at that point and working out its gradient using the same equation.

Question:

Label the journey shown below with the correct words by dragging them onto the graph.

These are similar to displacement-time graphs, but this time velocity is on the y-axis. Here are the only possibilities that you'll come across at A-level.

Notice that the gradient =

change in D (or ΔD) change in t (or Δt)

= the velocity at any time.

You also need to know that the area under the line gives you the displacement of the object up to that point.

Last, but not least, are the acceleration-time graphs!

Note: All three of the movement graphs are related to each other as the:

• Gradient of D/t graph gives you the points on the v/t graph.
• Gradient of v/t graph gives you the points on the a/t graph.