An object, moving with a speed of 6.25 m/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:

Question

Accepted Answer

2 s. dv/dt = -2.5*sqrt(v) -> integral v^(-1/2) dv = -2.5*integral dt -> 2*sqrt(v) = -2.5 t + C. At t=0, v=6.25 so C = 2*2.5 = 5. Setting v=0 gives 0 = -2.5 t + 5 -> t = 2 s.

An object, moving with a speed of 6.25 m/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:

Solution

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