Question

The energy required to accelerate a car from 10m/s to 20m/s is x times the energy required to accelerate the same car from 0 to 10m/s.calculate the value of x?

Answer 1

Increase in kinetic energy while accelerating from 0 m/s to 20 m/s is,

ΔKE₁ = ½ m(20²) - ½ m(0²) = 400[m/2]

Increase in kinetic energy while accelerating from 20 m/s to 40 m/s is,

ΔKE₂ = ½ m(40²) - ½ m(20²) = [m/2][1600 - 400] = 1200[m/2]
since no difference in potential energy (eg: height is not changing), So total energy is same as kinetic energy
So, from question we can write,
1200[m/2] = x * 400[m/2]
So,
x = 1200/400
x = 3
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