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Question

Draw a velocity-time graph for a body moving with an initial velocity u and uniform acceleration a. Use this graph to find the distance travelled by the body in time t.

Category: Motion in One Dimension ICSE

February 21, 2024

Answer

Below is the velocity-time graph for a body moving with an initial velocity u and uniform acceleration a:

Let v be the velocity at time t for this body having initial velocity u and uniform acceleration a as shown in the graph.

Distance travelled by the body in time t = Area under the velocity-time curve.

Hence,

Distance travelled = area of trapezium OABD

= $1\over 2$ Sum of parallel sides × height

= $1\over 2$ × (OA + DB) × OD

= $1\over 2$ × (u + v) × t

= $(u+v)t\over 2$

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