If the velocity of a body related to displacement $x$ is given by $v=\sqrt{5000+24 x} \mathrm{~m} / \mathrm{s}$, then the acceleration of the body is ______

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Kinematics

If the velocity of a body related to displacement

x

is given by

v = 5000 + 24 x m / s

, then the acceleration of the body is ______

Answer: 12

Solution

Using

v = 5000 + 24 x

, we have

v^{2} = 5000 + 24 x

. Differentiating both sides with respect to time:

2 v \frac{d v}{d t} = 24 \frac{d x}{d t}

Since

\frac{d v}{d t} = a

(acceleration) and

\frac{d x}{d t} = v

(velocity):

2 v a = 24 v

a = 12 m/s^{2}

JEE Main · 2021 · 27 Aug 2021 · Shift 1 · Integer answer

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