A moving body is covering distances which are proportional to square of the time. Then the acceleration of the body is (a) constant but not zero (b) increasing (c) zero (d) decreasing
Question
A moving body is covering distances which are proportional to square of the time. Then the acceleration of the body is (a) constant but not zero (b) increasing (c) zero (d) decreasing
Solution
The answer is (a) constant but not zero.
Here's why:
The problem states that the distance covered by the body is proportional to the square of the time. This implies that the body is moving with a uniformly accelerated motion, because in such motion, the distance covered is given by the equation:
s = ut + 0.5at^2
where: s = distance covered u = initial velocity t = time a = acceleration
Since the distance is proportional to t^2, it means that the term ut is zero or negligible. This implies that the initial velocity of the body is zero. So, the equation becomes:
s = 0.5at^2
This equation shows that the acceleration (a) is constant, because it is a coefficient of t^2. Therefore, the acceleration of the body is constant but not zero.
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