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 = 2m.

Easy

A

48ms^-2
B

80ms^-2
C

18ms^-2
D

10ms^-2

Solution

V = 3x² - 2x
$\frac{dv}{dt} = 6 x \frac{dx}{dt} - \frac{2 dx}{dt}$
a = 6 v x - 2 v
when x = 2 v = 8 m/s
a = 6 x 8 x 2 - 2 x 8
= 96 -16 = 80 m/s²

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