1) Draw velocity-time graph for an uniformly accelerated object. Using velocity-
time graph, derive second equation of motion,
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Question-
Derive the second equation of motion using a velocity-time graph
Answer-
Consider the linear motion of a body with an initial velocity u. Let the body accelerate uniformly and acquire a final velocity v after time t. The velocity-time graph is a straight line AB as shown below.
At t = 0, initial velocity = u = OA
At t = t, final velocity = v = OC
The distance S travelled in time t = area of the trapezium OABD
s = (1/2) x (OA + DB) × OD
s = (1/2) x (u + v) × t
Since v = u + at,
s = (1/2) x (u + u + at) × t
s = ut + (1/2) at²
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