A particle of mass moves along the x-axis from to

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

Problem

A particle of mass

1.5\,\text{kg}

moves along the x-axis from

x = 0

x = 10\,\text{m}

. The only horizontal force acting on it varies with position as follows: •

F = 3x^{2}\,\text{N}

for

0 \le x \le 4\,\text{m}

, •

F = -12\,\text{N}

for

4\,\text{m} < x \le 7\,\text{m}

, •

F = 6 - 2x\,\text{N}

for

7\,\text{m} < x \le 10\,\text{m}

(all

x

in metres). The particle has a speed of

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

at the origin. (i) Compute the work done on the particle in each of the three segments and hence find the net work done from

x = 0

x = 10\,\text{m}

. (ii) Using the work–energy theorem, determine the speed of the particle at

x = 10\,\text{m}

. (iii) Within the interval

4\,\text{m} < x \le 7\,\text{m}

, find (with calculation) whether the particle momentarily comes to rest. If so, state the position where this occurs.