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

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

#### Speed and Velocity

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

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!):

#### Displacement-time graphs

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.

#### Velocity-time graphs

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 V (or ΔV) change in t (or Δt) = the acceleration 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. #### Acceleration-time graphs

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.