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Question: The velocity of a particle at an instant is \(10 \mathrm {~ms} ^ { - 1 }\) . After 3 s its velocity ...

The velocity of a particle at an instant is 10 ms−110 \mathrm {~ms} ^ { - 1 } . After 3 s its velocity will becomes 16 ms−116 \mathrm {~ms} ^ { - 1 } . The velocity at 2 s, before the given instant will be

A

6 ms−16 \mathrm {~ms} ^ { - 1 }

B

4 ms−14 \mathrm {~ms} ^ { - 1 }

C

2 ms−12 \mathrm {~ms} ^ { - 1 }

D

1 ms−11 \mathrm {~ms} ^ { - 1 }

Answer

6 ms−16 \mathrm {~ms} ^ { - 1 }

Explanation

Solution

Here, u =10 ms−1= 10 \mathrm {~ms} ^ { - 1 } , t = 3 s , v = 16m S−1\mathbf { S } ^ { - 1 }

a=v−ut=16−103=2 ms−2\mathrm { a } = \frac { \mathrm { v } - \mathrm { u } } { \mathrm { t } } = \frac { 16 - 10 } { 3 } = 2 \mathrm {~ms} ^ { - 2 }

Now velocity at 2s, before the given instant

10=u+2×210 = u + 2 \times 2 (∵v=u+at)( \because v = u + a t )

∴y=6 ms−1\therefore \mathrm { y } = 6 \mathrm {~ms} ^ { - 1 }