JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Work, Power & Energy

A car accelerates from rest to

u m / s

. The energy spent in this process is E J. The energy required to accelerate the car from

u m / s

2 u m / s

is nE J. The value of

n

____

Answer: 3

Solution

Using the work-energy theorem:

Energy to accelerate from 0 to

u

E_{1} = \frac{1}{2} m u^{2} - 0 = \frac{1}{2} m u^{2} = E

Energy to accelerate from

u

2 u

E_{2} = \frac{1}{2} m (2 u)^{2} - \frac{1}{2} m u^{2} = 2 m u^{2} - \frac{1}{2} m u^{2} = \frac{3}{2} m u^{2} = 3 E

Therefore,

n = 3

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Integer answer

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