Posted by **muhammad** on Wednesday, April 25, 2012 at 3:49am.

a car of mass 'm'starts from rest and is driven with constant power.after some time it covers a distance 'x'.what should be the speed of car?how we can find the speed of car?

- physics -
**Damon**, Wednesday, April 25, 2012 at 6:38am
power = force * speed

p = F v

so

F = p/v

F = m a = p v

so

a = (p/m) v

or

dv/dt = (p/m) v

try form

v = b e^kt + c

dv/dt = b k e^kt

so k = p/m

so

v = b e^(p/m)t + c

at t = 0, v = 0

0 = b + c

so

v = b e^(p/m) t - b

at time t, it is at x

this requires solving differential equation of form

dx/dt = b e^kt - b

x = (b/k) e^kt - bt + c

at t = 0, x = 0

0 = (b/k) + c

so c = -b/k = -bm/p

x = (bm/k) e^(p/m)t - b t -bm/p

given an x at time t, solve for b

- error repair -
**Damon**, Wednesday, April 25, 2012 at 6:48am
power = force * speed

p = F v

so

F = p/v

F = m a = p/ v

so

a = p/(m v)

or

v dv/dt = (p/m)

v dv = (p/m) dt

v^2/2 = (p/m) t + constant which is zero

v^2 = (2p/m)t

v = (2 p t/m)^.5

- physics -
**Damon**, Wednesday, April 25, 2012 at 6:54am
dx/dt = (2 p /m)^.5 t^.5

let k = 2 p/m

dx/dt = k t^.5

dx = k t^.5 dt

x = (k/1.5) t^1.5 + c

when t = 0, x = 0 so c = 0

x = (4 p/3m) t^1.5

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