The distance travelled by a particle is related to time t as $\mathrm{x}=4 \mathrm{t}^{2}$. The velocity of the particle at $\mathrm{t}=$ 5 s is .

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Kinematics

The distance travelled by a particle is related to time t as

x = 4 t^{2}

. The velocity of the particle at

t =

5 s is .

(A) $40 ms^{- 1}$ ✓ Correct
(B) $25 ms^{- 1}$
(C) $20 ms^{- 1}$
(D) $8 ms^{- 1}$

Answer: (A)

Solution

The velocity is the rate of change of position,

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

. Differentiating

x = 4 t^{2}

gives

v = 8 t

, which at

t = 5 s

8 \times 5 = 40 m/s

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Single correct option

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