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Question

A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time t is given by s=t2+atb+17, where a,b are real numbers. If the particle comes to rest after 5 sec at a distance of s=25 units from the fixed point, then values of a and b are respectively

A
10,33
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B
10,33
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C
8,33
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D
10,33
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Solution

The correct option is B 10,33
When the particle comes to rest, then its velocity is zero. The velocity of the particle is,
dsdt=2t+a
At t=5 sec
0=2×5+a
a=10

And at t=5 sec, distance, s=25
Substitute the values in the equation, s=t2+atb+17
25=52+(10)×5b+17
b=33

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