A cart on a horizontal frictionless track experiences a piecewise constant horizontal…

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

1.2\,\text{kg}

cart on a horizontal frictionless track experiences a piecewise constant horizontal force described below (positive is to the right): •

F = +4.0\,\text{N}

for

0 \le t < 2.0\,\text{s}

•

F = -2.0\,\text{N}

for

2.0 \le t < 6.0\,\text{s}

•

F = 0

for

t \ge 6.0\,\text{s}

t=0

the cart is at rest. (a) Calculate the cart’s speed at

t = 2.0\,\text{s}

. (b) Calculate the cart’s speed at

t = 6.0\,\text{s}

. (c) Derive a piecewise expression for the cart’s linear momentum

p(t)

for the entire interval

0 \le t \le 6.0\,\text{s}

. (d) Sketch a graph of

p(t)

versus

t

for

0 \le t \le 6.0\,\text{s}

, clearly labeling key values and explaining how specific features of the force–time description are reflected in your graph.