## Velocity Time Graphs

A velocity time graph is a graph of time on the x axis plotted against velcity on the y axis.

Velocity time graphs have two very important features:

The area under the graph represents the displacement from the start point.

The gradient of the graph at any point is the acceleration at that point. It the graph slopes up the velocity is positive. If the graph slopes down the velocity is negative.

The diagram above shows the motion of a car between two sets of traffic lights.

The initial acceleration is the slope of the graph when

The final acceleration is the slope of the graph between

The area under the graph, hence the distance travelled can be used as a condition.

The diagram illustrates the motion of two cars. One car is stationary at traffic lights and when the lights turn green it starts to accelerate, moving with constant acceleration untilAnother car starts to accelerate at the same time but whenit changes, to move with constant velocity. Atthe second car has travelledmore than the first. Find