Question

The force resisting the motion of a car is taken as being proportional to the square of the car’s
speed. The magnitude of the force at a speed of 20 m s–1 is 800 N.
What effective power is required from the car’s engine to maintain a steady speed of 40 m s–1?
The Available Answers Are:
A 32 kW B 64 kW C 128 kW D 512 kW

Answer 1

The solution to the problem is as follows:

Given Ff α v^2 

=>Ff = kv^2 
=>800 = k x (20)^2 
=>k = 2 

2nd condition:- 
=>Ff = kv^2 
=>Ff = 2 x (40)^2 
=>Ff = 3200 N 

At constant speed=>a = 0=>F(net) = 0 

By F(net) = F(applied) - F(friction) 
=>Fa = Ff = 3200 N 

Thus by P = Fv 
=>P = 3200 x 40 
=>P = 128000 Watt OR 128 kW


I hope my answer has come to your help. God bless and have a nice day ahead!