Velocity-time graph

• A velocity-time graph is a graph which shows:
  • the velocity of an object on the y-axis
  • the time on the x-axis.
• They tell us how fast an object is moving, and in which direction, over a period of time.

Finding the displacement

The displacement from one point in time to another point in time is the area under the graph between those times.

We can find the area under a graph using either integration if we know the equation of the graph, or by drawing triangles and rectangles (or trapeziums) and estimating the area that way.

Finding the velocity at a specific time

The velocity at a specific time is the value of the graph at that time.

We can find this by reading off the graph at that time, just like we would with a distance-time graph or a displacement-time graph.

Finding the acceleration

The acceleration at a specific time is the gradient of the graph at that time.

We can find the gradient by drawing a tangent to the curve at that point, and then finding the gradient of that tangent.

Or, we can just find the derivative if we know an equation for the graph.

Finding the average acceleration

The average acceleration between two points in time is the change in velocity divided by the change in time.

We can find this by finding the velocity at each of those times, and then using the normal acceleration formula to find the average acceleration.