A cart on a smooth horizontal track is acted upon by a horizontal force that varies…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

4.0\,\text{kg}

cart on a smooth horizontal track is acted upon by a horizontal force that varies with time as follows: • For

0 \le t \le 2\,\text{s}

, the force is constant at

+10\,\text{N}

. • For

2\,\text{s} < t \le 6\,\text{s}

, the force is constant at

-5\,\text{N}

(opposite direction). Assume the cart starts from rest at

t = 0

. (i) Find the impulse delivered to the cart in the first

2\,\text{s}

and in the next

4\,\text{s}

separately. Hence obtain the net impulse from

t = 0

t = 6\,\text{s}

. (ii) Determine the velocity of the cart at

t = 6\,\text{s}

. (iii) Calculate the maximum speed attained by the cart during the motion and specify the time at which this occurs.