Physics

Problem

The displacement

x

(in metres) of a particle moving along a straight line varies with time

t

(in seconds) as described below: • For

0 \leq t \leq 5\,\text{s}

, displacement increases uniformly from

0\,\text{m}

10\,\text{m}

. • For

5\,\text{s} < t \leq 10\,\text{s}

, displacement increases from

10\,\text{m}

40\,\text{m}

with constant acceleration. • For

10\,\text{s} < t \leq 13\,\text{s}

, displacement remains constant at

40\,\text{m}

. Answer the following: a. (i) Draw the position–time (

x

–

t

) graph representing the motion for the interval

0 \leq t \leq 13\,\text{s}

. b. (ii) From the graph, determine the instantaneous velocity of the particle at

t = 5\,\text{s}

. c. (iii) Determine the magnitude of the constant acceleration during the interval

5\,\text{s} < t \leq 10\,\text{s}

. d. (iv) Draw the corresponding velocity–time (

v

–

t

) graph for the complete

13\,\text{s}

of motion.

Intuitive explanation

This problem asks you to extract motion information from a piecewise displacement description—the key is recognizing that each segment has a different kinematic character. In the first phase, uniform increase means constant velocity; in the second, you'll need to find the acceleration from the change in displacement and time; in the third, no change means zero velocity. Sketch or write out the $x$ – $t$ relationship for each interval, then use slopes and curvature to find velocity and acceleration in each region.

Intuitive explanation

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