f a 1300 kg car can accelerate from 35 km/h to 65 km/h in 4.3 s, how long will it take to accelerate from 65 km/h to 95 km/h?  Assume the power stays the same, and neglect friction losses.

Weight of the car is kg.

Car accelerate from 35 kmph to 65 kmph in 4.3 sec.

Find the time when car accelerates from 65kmph to 95 kmph.

Kinetic energy of the car is .

Resultant kinetic energy 35 kmph to 65 kmph:

Power is rate of energy with respect to time.

Substitute and in the above expression.

.

Resultant kinetic energy from 65 kmph to 95 kmph.

Initial kinetic energy at kmph:  J.

Ending kinetic energy at kmph:  J.

Let the time taken by the car to accelerate from 65kmph to 95 kmph as sec.

Power stays in car during to is

Power remains in both cases are same.

From (1) and (2) ,

Therefore, time taken by the car to accelerate from 65kmph to 95 kmph is sec.

Power is defined as .

where and .

Integrating on each side.

As power remains same and mass is constant, thus expression canbe written as

, where are constants.

At the initial stage .

At  sec, speed of the car is increased from 35 kmph to 65 kmph, kmph.

Find the time when car accelerates from 65kmph to 95 kmph.

Substitute , and in .

.

Kinetic energy