A particle starts from the origin at and moves along a straight line as described…

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

Problem

A particle starts from the origin at

t=0\,\text{s}

and moves along a straight line as described below: • From

t = 0\,\text{s}

t = 4\,\text{s}

it moves with a constant velocity of

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

. • From

t = 4\,\text{s}

t = 8\,\text{s}

it moves with a constant acceleration of

2\,\text{m s}^{-2}

in the same direction, its velocity at

t = 4\,\text{s}

being

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

. (i) Determine the displacement of the particle at

t = 0\,\text{s}

4\,\text{s}

6\,\text{s}

and

8\,\text{s}

. (ii) Using the results of part (i), sketch a qualitative displacement–time graph for the motion from

t = 0\,\text{s}

t = 8\,\text{s}

, marking all calculated points clearly. (iii) Calculate the instantaneous velocity of the particle at

t = 6\,\text{s}

. (iv) Compute the average velocity for the entire interval

0\,\text{s}

8\,\text{s}

. (v) Compare the values obtained in parts (iii) and (iv) and state, with reason, whether they are equal or different.