First slide

Instantaneous acceleration

Question

For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3x² - 2x, then what is the acceleration at x = 2 m.

Easy

A

48 ms^-2
B

80 ms^-2
C

18 ms^-2
D

10 ms^-2

Solution

$Given v = 3 x^{2} - 2 x; differentiating v, we get \frac{dv}{dt} = (6 x - 2) \frac{dx}{dt} = (6 x - 2) v \Rightarrow a = (6 x - 2) (3 x^{2} - 2 x) Now put x = 2 m \Rightarrow a = (6 \times 2 - 2) (3 (2)^{2} - 2 \times 2) = 80 {ms}^{- 2}$

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