The velocity of a body moving along the -axis is described by the quadratic function

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

Problem

The velocity of a body moving along the

x

-axis is described by the quadratic function

v(t)=ut-\tfrac12 bt^2+c

, where

u=6\,\text{m\,s}^{-2}

b=2\,\text{m\,s}^{-3}

and

c=4\,\text{m\,s}^{-1}

; the motion is considered for

t\ge0

. (i) Derive an expression for the instantaneous acceleration as a function of time. (ii) Show that the acceleration becomes zero at a time

t_0

and obtain

t_0

in terms of

u

and

b

. Then evaluate

t_0

for the given numerical values. (iii) Determine the velocity and the displacement from

t=0

t=t_0

. (iv) Using the sign of acceleration and velocity, identify the intervals of time during which the body is speeding up and those during which it is slowing down.

Related theory

Applications of Integration
Motion
Rates of change
Rate of change of quantities

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