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

Question

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

TestHub · Accepted Answer

d t d v ​ = − 2.5 v ​ Integrating the above equation. ⇒ 2 v ​ = − 2.5 t + C at t = 0 , v = 6.25 ⇒ C = 5 at v = 0 ⇒ t = 2.5 5 ​ = 2 s

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