A trolley moves on a straight horizontal track

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

A trolley moves on a straight horizontal track. A laboratory marker

M

is taken as the origin

O

, and the positive

x

-direction is chosen toward the east. (i) At

t = 0\,\text{s}

the trolley is at

x_1 = 12\,\text{m}

. After

5\,\text{s}

it reaches

x_2 = 38\,\text{m}

. Calculate the displacement and average velocity of the trolley in this frame. (ii) An observer standing

30\,\text{m}

east of

M

sets up his own origin

O'

at his position, keeping the same positive eastward direction. Find the coordinates

x'_1

and

x'_2

of the trolley at the two instants in this new frame. (iii) Using the results of parts (i) and (ii), verify that the trolley’s displacement and average velocity have identical values for both observers. (iv) State, with reason, whether the two observers can ever disagree on the total path length travelled by the trolley between the two instants.

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