Plot a velocity-time graph to describe the motion of a body with an example. Explain how you can compute the distance moved by the body in a given time from its velocity-time graph.
Let us consider a body moving in uniform motion, then we can plot the velocity-time graph for the motion of the body moving with a constant velocity of 30 km/h, which means that the body will cover a distance of 30 km in1 hour, 60km in 2 hours, 90 km in 3 hours and so on.
If we want to know the distance the body has moved between time say t1 and t2. We draw perpendiculars from points corresponding to the time t1 and t2 on the above graph. The two perpendiculars enclose a rectangle ABCD between the graph and the time axis. The sides AB and CD of this rectangle are equal to (t2 – t1) while the sides AC and BD are equal to 30 km/h. We know that the distance s covered by a body moving a velocity v, in time t is given by
s = vt
Hence, the distance moved by the body in time (t2 – t1) is
= [(30 km/h)(t2 – t1)h]
= 30 (t2 – t1) km
The area under the velocity-time graph gives the distance travelled by the body.
If we want to know the distance the body has moved between time say t1 and t2. We draw perpendiculars from points corresponding to the time t1 and t2 on the above graph. The two perpendiculars enclose a rectangle ABCD between the graph and the time axis. The sides AB and CD of this rectangle are equal to (t2 – t1) while the sides AC and BD are equal to 30 km/h. We know that the distance s covered by a body moving a velocity v, in time t is given bys = vt
Hence, the distance moved by the body in time (t2 – t1) is
= [(30 km/h)(t2 – t1)h]
= 30 (t2 – t1) km
The area under the velocity-time graph gives the distance travelled by the body.
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