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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 v1 be the velocity at time t1 and v2 be the velocity at time t2.  

Now, Acceleration = change in velocity/time interval

= (final velocity - initial velocity) / time interval
= (v2 - v1) / (t2 - t1)= Δv / Δt
= AB / BC which is the slope of the graph

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

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.


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