A particle moves along a straight line for seconds

PHYSICS · Single correct · CBSE · Physics · Motion · Motion

Problem

A particle moves along a straight line for

0\le t\le10

seconds. Its velocity is a constant

4\text{ m/s}

for

0\le t<5

and a constant

-4\text{ m/s}

for

5\le t\le10

. Which statement best explains why the particle’s average velocity on

[0,10]

0\text{ m/s}

even though its speed is never

0\text{ m/s}

? (a) Because the particle traveled equal distances in opposite directions, the total distance is

0

, so the average velocity is

0\text{ m/s}

." (b) Equal positive and negative displacements on the two 5-second subintervals cancel, giving a net displacement of

0\text{ m}

and thus an average velocity of

0\text{ m/s}

." (c) Average velocity depends only on the velocity values at the endpoints of the interval; since

v(0)=4

and

v(10)=-4

, their sum is

0

, so the average velocity is

0\text{ m/s}

." (d) The velocity changes sign exactly at

t=5

, so the particle must momentarily stop there; spending equal time before and after that stop forces the average velocity to be

0\text{ m/s}