Rankers Physics
Topic: Kinematics
Subtopic: Equations of Motion

A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th second to that covered in 5 s in
9/25
3/5
25/5
1/25

Solution:

For a body starting from rest with constant acceleration:

- Distance covered in the 5th second: \( s_5 = u + \frac{a}{2}(2n - 1) \), where \( u = 0 \) and \( n = 5 \):
\[
s_5 = \frac{a}{2} (9) = \frac{9a}{2}
\]

- Distance covered in 5 seconds: \( S = \frac{1}{2} a t^2 \), where \( t = 5 \):
\[
S = \frac{1}{2} a (5)^2 = \frac{25a}{2}
\]

Ratio of distances:
\[
\frac{s_5}{S} = \frac{\frac{9a}{2}}{\frac{25a}{2}} = \frac{9}{25}
\]

Thus, the ratio is 9:25.

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