The acceleration of a particle is defined by the relation a = -k√v, where k is constant. Knowing that x = 0 and v = 81 m/s at t = 0 and v = 36 m/s x = 18 m determine (a) the velocity of the particle when x = 24 m (b) the time required for the particle to come to rest.
greenjie greenjie 22-25, M 2 Answers Jan 5, 2013 in Education

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you know a = dv/dt . it can also be written as dv/dx * dx/dt. where x is the distance. so your dx/dt is nothing but v. To sum up. a = v*dv/dx = -ksqurt(v). Now you can integrate it . the limits for x are 0 to 18. and v are 81 to 36. becareful with the signs. after ur done . you get the value of k. and also u get the equation of velocity vrs distance.

a)substitute x = 24 , in the quation and u will get the velocity.

b) you know velocity = dx/dt. intergrate it , u will get the time.

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thx so much

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its okay.

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