Consider a particle that moves along a straight line such that at time its…

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Consider a particle that moves along a straight line such that at time

t_1

its displacement is

x_1

and at a later time

t_2

(t_2 > t_1)

its displacement is

x_2

. The displacement–time graph between

t_1

and

t_2

may have any shape. (i) Derive an expression for the average velocity of the particle for the interval

t_1

t_2

in terms of

x_1

x_2

t_1

, and

t_2

. (ii) Explain why the expression obtained in part (i) is equivalent to the slope of the straight line joining the two points

(t_1, x_1)

and

(t_2, x_2)

on a displacement–time graph. (iii) A car is at

x = -15\,\text{m}

t = 2\,\text{s}

and at

x = 45\,\text{m}

t = 14\,\text{s}

. Using the result of part (i), calculate its average velocity for this time interval and comment on its direction. (iv) If the same car returns to the origin

(x = 0)

t = 20\,\text{s}

, find its average velocity and average speed for the entire journey from

t = 2\,\text{s}

t = 20\,\text{s}

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