Question

A 3.0 kg toy car can move along an x axis; the figure gives F_x of the force acting on the car, which begins at rest at time t=0. The scale on the F_xs axis is such that the point F_xs = 15.0 N. What is p at (a) t = 4.0 s and (b) t = 9.0 s? (c) What is v at t = 4.0 s and (d) t = 9.0 s?

Answer 1

From Newton's second law of motion:

$F = \frac{\mathrm{d} P}{\mathrm{d} t}$

.where P is momentum and t is time, F is force. Hence,

$P = \int_{0}^{t_0} F \mathrm{d} t$

a) t = 4 s.

P = area under curve from t = 0s to t = 4s.

P = 0.5*(4+2)*30 = 90 N s.

b) t = 9 sec.

P = 0.5*(6+2)*30-0.5*(3+1)*15 = 120-30 = 90 Ns.

c) velocity at t = 4s,

v = P/m = 90/3 = 30 m/s

d) velocity at t = 9s.

v = P/m = 90/3 = 30 m/s.