First slide

Position Path Length (Distance) And Displacement

Question

The displacement ‘x’ (in meter) of a particle of mass ‘m’ (in kg) moving in one dimension under the action of a force, is related to time ‘t’ (in sec) by $t = \sqrt{x} + 3$ . The displacement of the particle when its velocity is zero, will be

Moderate

A

4 m
B

0 m (zero)
C

6 m
D

2 m

Solution

$Given : t = \sqrt{x} + 3 O r \sqrt{x} = t - 3$
Squaring both sides, we get
$x = (t - 3)^{2} Velocity, v = \frac{d x}{d t} = \frac{d}{d t} (t - 3)^{2} = 2 (t - 3)$
Velocity of the particle becomes zero, when
$2 (t - 3) = 0 or t = 3 s At t = 3 s x = (3 - 3)^{2} = 0 m$

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