A particle moves along a straight line such that its displacement (in metres) from a…

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A particle moves along a straight line such that its displacement

s

(in metres) from a fixed origin

O

at time

t

seconds is denoted by a differentiable function

s=f(t)

. Answer the following questions with proper justification. (i) Define the instantaneous velocity of the particle in terms of

s

and

t

. State the physical meaning of a positive and a negative value of this quantity. (ii) The displacement of the particle is given by

s=3\cos(2t)

for

0\le t\le\pi

. Obtain an expression for the velocity

v(t)

. (iii) Using your result of part (ii), determine the sub-intervals of

[0,\pi]

during which the particle is moving (a) away from the origin, and (b) towards the origin. Explain your reasoning by referring to the sign of

v(t)