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Motion in A Plane

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Physics Part I

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Class 10 Class 12

An object moving with a speed of 6.25m/s, is decelerated at a rate given by dv/dt =- 2.5√v, where v is the instantaneous speed. The time taken by the object, to come to rest, would be

  • 2 s

  • 4 s

  • 8 s

  • 1 s


A.

2 s

dv over dt space equals space minus space 2.5 square root of straight v
fraction numerator dv over denominator square root of straight v end fraction space equals space minus 2.5 dt
integral subscript 6.25 end subscript superscript 0 straight v to the power of negative 1 divided by 2 end exponent space dv space equals space minus 2.5 integral subscript 0 superscript straight t dt
minus 2.5 left square bracket straight t right square bracket subscript 0 superscript straight t space equals space left square bracket 2 space straight v to the power of 1 divided by 2 end exponent right square bracket subscript 6.25 end subscript superscript 0
straight t space equals 2 straight s
dv over dt space equals space minus space 2.5 square root of straight v
fraction numerator dv over denominator square root of straight v end fraction space equals space minus 2.5 dt
integral subscript 6.25 end subscript superscript 0 straight v to the power of negative 1 divided by 2 end exponent space dv space equals space minus 2.5 integral subscript 0 superscript straight t dt
minus 2.5 left square bracket straight t right square bracket subscript 0 superscript straight t space equals space left square bracket 2 space straight v to the power of 1 divided by 2 end exponent right square bracket subscript 6.25 end subscript superscript 0
straight t space equals 2 straight s
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