Answer :
Answer:
The time taken by the car with a useful power output is 4.03 seconds.
Explanation:
Given that,
Mass of the car, m = 875 kg
Initial speed of the car, u = 0
Final speed of the car, v = 17 m/s
Power of the car, P = 42 hp = 31332 W
The power output of the car is given by the work done per unit time. It is given by :
[tex]P=\dfrac{W}{t}[/tex]
Initial kinetic energy of the car will be 0 as it is at rest.
Final kinetic energy of the car is :
[tex]K=\dfrac{1}{2}mv^2[/tex]
[tex]K=\dfrac{1}{2}\times 875\times (17)^2[/tex]
K = 126437.5
As per the work energy theorem, the change in kinetic energy of the object is equal to the work done.
So,
[tex]P=\dfrac{W}{t}[/tex]
[tex]t=\dfrac{W}{P}[/tex]
[tex]t=\dfrac{126437.5}{31332}[/tex]
t = 4.03 seconds
So, the time taken by the car with a useful power output is 4.03 seconds. Hence, this is the required solution.