# How is displacement found from a velocity time graph?

Jul 13, 2015

Area under the velocity time graph

#### Explanation:

The velocity time graph has two axis - the velocity along the y-axis and time along the x-axis. both velocity as well as time are physical quantities.

Whenever we have physical quantities along the axis (velocity-time in this instance) find the product or ratio of the two quantities - if they correspond to another derived quantity we use the identity to find it.

e.g. in a velocity-time graph dividing velocity by time is acceleration therefore $\frac{\Delta y}{\Delta x}$ (slope of curve) should give acceleration.

Similarly in a velocity-time graph multiplying velocity by time is distance therefore $\left(\Delta y\right) \times \left(\Delta x\right)$ (area under curve) should give distance.

We do not say displacement as the product does not account for direction.