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Question

A stone is falling freely and describes a distance S in t seconds given by equation S=12gt2. The acceleration of the stone is


A

Uniform

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B

Zero

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C

Non–uniform

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D

Indeterminate

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Solution

The correct option is A

Uniform


Step 1. Given Data:

Distance covered by stone, S=12gt2

Time =t

Acceleration of the stone =a

Step 2. Find the acceleration of the stone:

We have,

S=12gt2 Given …..i

Where S is distance, g acceleration due to gravity and t is time.

Now,

Differentiate equation i with respect to the time we get

dSdt=d12gt2dt

Where dSdt is the velocity of the stone.

dSdt=v=gt ……..ii

Where v is the velocity of the stone.

Again, differentiate equation ii with respect to the time we get.

dvdt=dgtdt

dvdt=a=g

a=constant

Therefore, the acceleration of the stone is uniform.

Hence, option A is correct.


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