First slide

Instantaneous acceleration

Question

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

Easy

A

x²
B

e^x
C

x
D

log e^x

Solution

According to question :
$\frac{du}{dt} \propto x$
$or \frac{du}{dx} \cdot \frac{dx}{dt} \propto x$
$or \frac{du}{dx} \cdot u \infty x$
$or udu \propto xdx$
$or v^{2} \propto x^{2}$

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