The area under velocity time graph during the interval 0 to t is ABDO. The velocity-time graph of such a motion is as shown in figure 5. Let v 0 be the velocity of the particle at the instant t = 0 and v t at a later instant t. The area under the velocity-time graph gives the total displacement of the particle during the time interval.Ĭonsider a particle moving along a straight line with uniform acceleration a. A) Area under the velocity-time graph gives the displacement The velocity-time graph of a particle moving along a straight line with uniform acceleration may be used to measure the displacement of the particle and also the acceleration. In figure 4, the ordinate OA gives the initial velocity and the ordinate BD gives the final velocity. If the particle has an initial velocity the graph will be a straight line, but will not pass through the origin as shown in figure 4. If the particle starts from rest and experiences uniform acceleration, the velocity-time graph will be a straight line passing through the origin and having a positive slope (as shown in figure 3) Figure 3 Velocity-Time graph for uniformly accelerated motion You can also go through my previous article which discussed the meaning and shape of the position-time graph for uniform motion. I.e, Area under the velocity-time graph of a particle will give the displacement of the body during that time interval. This means that the displacement of an object in the time interval (t 2 – t 1) is numerically equal to the area under the velocity-time graph between instants t 1 and t 2. The displacement of the particle in the time interval (t 2 –t 1) = velocity × time interval Let A and B be two points on the velocity-time graph corresponding to instants t 1 and t 2. The area under the velocity-time graph between the time t 1 and t 2 (shaded portion ) gives the displacement during the time interval t 1 to t 2 (figure 2). The velocity-time graph enables one to calculate the total displacement of the particle in a time interval. What does the area under a velocity graph represent? Similarly, if the particle moves with a uniform negative velocity, the velocity-time graph will be a straight line below the time axis. For a particle moving with uniform velocity, the graph is a straight line (AB) parallel to the time axis (X-axis) as shown in figure 1. In uniform motion, the velocity of the particle remains the same.
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