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 to 2u m/s is nE J. The value of n is ____________. Numerical answer type. Work it out, then open the answer.

Answer: 3. Energy spent = gain in KE. 0 → u: E = 1/2mu² u → 2u: 1/2m(4u² - u²) = 3 × 1/2mu² = 3E n = 3

A car accelerates from rest to u m/s. The energy spent in this… | JEE Main 2023 (13 Apr, Shift 2)

Q8JEE Main 2023 · 13 APR · SHIFT 2Easy

Kinetic Energy & Momentum

A car accelerates from rest to $u\text{ m/s}$ . The energy spent in this process is E J. The energy required to accelerate the car from $u\text{ m/s}$ to $2u\text{ m/s}$ is $nE\text{ J}$ . The value of $n$ is ____________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 3

Energy spent = gain in KE.
$0 \to u$ : $E = \frac{1}{2}mu^2$
$u \to 2u$ : $\frac{1}{2}m(4u^2 - u^2) = 3 \times \frac{1}{2}mu^2 = 3E$
$n = 3$

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