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 2 u m / s is nE J. The value of n is ____________.

Solution

Physics sir · 3 steps

Energy goes as v², so doubling the speed needs four times the energy, and E of it is already spent.

1. First stage. By the work-energy theorem, the energy spent equals the gain in kinetic energy. From rest to u: E = 1/2mu² - 0 = 1/2mu².
2. Second stage. From u to 2u the gain is the final kinetic energy minus the starting one, not just the final value.

   nE = 1/2m(2u)² - 1/2mu² = 4E - E = 3E

3. So. The second stage needs 3E joules, so n = 3.

The common slip: 4. Taking the full kinetic energy at 2u instead of the change gives 4, not 3. The car already had E at speed u.

The idea to keep. Kinetic energy grows as the square of speed. Equal steps in speed cost more and more energy, and you always pay only the difference in 1/2mv².

Answer from the NTA final answer key. Solution by PrepWiser.