Physics

Problem

A rocket-propelled sled of mass

m

starts from rest on a long, horizontal, frictionless track. From the instant

t=0

, the rocket engine delivers a constant mechanical power

P

to the sled. a. Derive an expression for the speed

v(t)

of the sled as a function of time. b. Using your result from part (a), obtain an expression for the distance

x(t)

the sled has traveled after time

t

. c. Determine the sled’s acceleration

a(t)

in terms of the given quantities and time. d. For

m = 5.0\times 10^{2}\,\text{kg}

and

P = 5.0\times 10^{4}\,\text{W}

, calculate the time required for the sled to reach a speed of

40\,\text{m\,s}^{-1}

. Express your answer to two significant figures.