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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.

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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