The velocity-time graph of a body is given. What quantities are represented by (a) slope of the graph and (b) area under the graph?​

a) acceleration

b) displacement

Explanation:

The velocity-time graph is a graph of velocity versus time. The velocity (m/s) would be on the Y-axis while time (s) would be on the X-axis.

a) The slope of a graph is given by: change in Y-axis/change in X-axis = ΔY/ΔX

In a velocity-time graph, ΔY = change in velocity and ΔX = change in time.

Hence, the slope of a velocity-time graph becomes: change in velocity/change in time.

Also, acceleration = change in velocity/change in time.

Hence, the slope of a velocity-time graph = acceleration.

b) Assuming that the area under a velocity-time graph is a rectangle, the area is given as:

Area of a rectangle = length x breadth

                                  = velocity x time (m/s x s)

Also, displacement = velocity x time (m)

Hence, the area under a velocity-time graph of a body would give the displacement of the body.

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

well clustered together.

points close on a scatter diagram