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A particle experiences constant acceleration for $20 s$ after starting from rest. If it travels a distance $X_{1}$ , in the first $10 s$ and the distance $X_{2}$ , in the remaining $10 s$ , then which is correct?

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X_{1} = 2 X_{2}

{X_{1} = X_{2}}^{}

X_{1} = 3 X_{2}

None of these

answer is D.

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Detailed Solution

A particle moves at a constant acceleration for

20 s

after starting from rest. If it travels a distance

X_{1}

, in the first

10 s

and a distance

X_{2}

, in the remaining

10 s

, then none is correct in the given options.
We know that

s = ut + \frac{1}{2} a t^{2}

Where

s =

distance,

u =

initial velocity,

a =

acceleration and

t =

time
Let “

a

” be the velocity at

t = 1 \sec

Then for the first

10 seconds

, as the particle starts moving from rest then

u = 0

⇒

X_{1} = 0 \times t + \frac{1}{2} a \times 100

⇒

X_{1} = 50 a

Now after 10 seconds the velocity becomes

10 a

,
By using the formula

v = u + at

⇒

X_{2} = 10 \times a \times 10 + \frac{1}{2} \times a \times 100

⇒

X_{2} = 150 a

Therefore,

X_{2} = 3 X_{1}

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