First slide

Instantaneous acceleration

Question

The position x of a particle varies with time (t) as x = a t² - b t³ . The acceleration at time t of the particle will be equal to zero

Moderate

A

$\frac{2 a}{3 b}$
B

$\frac{a}{b}$
C

$\frac{a}{3 b}$
D

zero

Solution

Given that $x = {at}^{2} - {bt}^{3}$
$∴$ velocity $= \frac{dx}{dt} = 2 at - 3 {bt}^{2}$
and acceleration $= \frac{d}{dt} (\frac{dx}{dt}) = 2 a - 6 bt$
$∴ t = \frac{2 a}{6 b} = \frac{a}{3 b}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App