# Velocity - Time Graph

Suppose, a car moving on a straight road starts from rest and speeds up to a constant acceleration of 5ms^{-2}. This means that the velocity of the car increases by 5 m per second in each second.

In these, the velocities are plotted, taking time along the x-axis and velocity along the y-axis. The plots lie on a straight line. This is the velocity-time graph of a uniformly accelerated motion of an object starting from rest, i.e. zero initial velocity.

Slope of Velocity - Time Graph determines acceleration

Referring to the graph, let v

_{1}be the velocity at time t

_{1}and v

_{2 }be the velocity at time t

_{2.}

Now, Acceleration = change in velocity/time interval

= (final velocity - initial velocity) / time interval

= (v_{2} - v_{1}) / (t_{2} - t_{1})= Î”v / Î”t

= AB / BC which is the slope of the graph

Thus, acceleration is given by the slope of the velocity-time graph.

Note

Since the car is travelling on a straight road, the direction of its velocity remains unchanged. The acceleration, in this case, results from a change in speed. Thus, for motion in a straight line, the velocity-time graph is the same as the speed-time graph.

If the car is not at rest initially but is travelling with a uniform velocity of say 10 ms^{-1}, i.e. its velocity at time t = 0 is 10 ms^{-1}, the velocity-time graph will not start at the origin. In this case, also, acceleration = AB / BC, the slope of the graph.