Question

An older-model car accelerates from 0 to speed v in a time interval of Δt. A newer, more powerful sports car accelerates from 0 to 5v in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars, compare the power of the two cars.

Answer 1

The power of sports car is 25 times power of older model car

Step-by-step explanation:

Consider mass of the two cars are same and is denoted by m.

Kinetic energy of older model car is determine by the relation:

`E_(1)= (1)/(2)mv^(2)`

Kinetic energy of sports car is determine by the relation:

`E_(2)= (1)/(2)m(5v)^(2)`

`E_(2)= 25(1)/(2)mv^(2)`

`E_(2)=25 E_(1)` ....(1)

Power is defined as energy per unit time.

According to the problem, the car has only kinetic energy. So, the power of old model and sports car are determine by the relation:

`P_(1)=(E_(1) )/(\Delta t)` and
`P_(2)=(E_(2) )/(\Delta t)`

Here P₁ and P₂ are the power of old model and sports car respectively.

The ratio of power of these car is:

`(P_(2))/(P_(1) ) =(E_(2))/(\Delta t)*(\Delta t)/(E_(1))`

`(P_(2))/(P_(1)) =(E_(2))/(E_(1))`

Substitute equation (1) in the above equation.

`(P_(2))/(P_(1)) = (25E_(1))/(E_(1))`

`(P_(2))/(P_(1)) =25`