(Work, Power, Energy Question) A car working at a rate 500W has a maximum speed 20 m/s when travelling...?

Question

...on the level against resistance proportional to the square if its speed. At what rate would the car have to work to double its maximum speed?

Answer 1

Power = force*velocity so
500 =20*f so the force is 25N
This force overcomes a resistance R=k*v^2
so
25=k*400 and k = 25/400
The new force needed is
F = 25/400*(40)^2 and the power is
P= 25/400*40^3=4000 watt