A particle is moving in a straight line according to equation x = 3 t 3 − 2 5 t 2 + 6 t . The time interval in which velocity i.e. instantaneous rate of change of position w.r.t. time is negative is

Instantaneous rate of change of x w.r.t. t d t d x = t 2 − 5 t + 6 < 0 ⇒ ( t − 2 ) ( t − 3 ) < 0 ⇒ 2 < t < 3

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PhysicsKinematics1-DEasy2 minQB

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A particle is moving in a straight line according to equation $x = \frac{t ^{3}}{3} - \frac{5}{2} t^{2} + 6 t$ . The time interval in which velocity i.e. instantaneous rate of change of position w.r.t. time is negative is

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Solution:

Instantaneous rate of change of x w.r.t. t

$\frac{d x}{d t} = t^{2} - 5 t + 6 < 0 \Rightarrow (t - 2) (t - 3) < 0 \Rightarrow 2 < t < 3$

Stream:JEESubject:PhysicsTopic:KinematicsSubtopic:1-D

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