First slide

Instantaneous acceleration

Question

A body sliding on a smooth inclined plane requires 4 second to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top ?

Easy

A

1s
B

2s
C

4s
D

16s

Solution

Time taken by the body to reach the bottom t₁,= 4 sec. Let t₂ be the time to cover one-fourth distance.
Initial distance s₁ = s ond final distance s₂ = s/4
We know that $s = \frac{1}{2} {gt}^{2} or t \propto \sqrt{s}$
$\begin{array}{ll} ∴ \frac{t_{1}}{t_{2}} = \sqrt{(\frac{s_{1}}{s_{2}})} = \sqrt{[\frac{s}{(s / 4)}]} = \sqrt{4} = 2 \\ or t_{2} = \frac{t_{1}}{2} = \frac{4}{2} = 2 \sec \end{array}$

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