Suppose that the acceleration of a model rocket is proportional to the difference between 160 ft/sec and the rocket's velocity. If it is initially at rest and its initial acceleration is 280 ft/sec22, how long will it take to accelerate to 128 ft/s

Explanation:

Given ,

dv / dt = k ( 160 - v )

dv / ( 160 - v ) = kdt

ln ( 160 - v ) = kt + c , where c is a constant

when t = 0 , v = 0

Putting the values , we have

c = ln 160

ln ( 160 - v ) = kt + ln 160

ln ( 160 - v / 160 ) = kt

(160 - v ) / 160 =

1 - v / 160 =

v / 160 = 1 -

v = 160 ( 1 - )

differentiating ,

dv / dt = - 160k

acceleration a   = - 160k

given when t = 0 , a = 280

280 = - 160 k

k = - 175

a = - 160 x - 175

a = 28000

when a = 128  t = ?

128 = 28000

= .00457

f=ma newton

f=100x2.5=250n

this could be newton#'s law of cooling. the cooling curve is exponential