# How do I understand why the maximum speed of this car stays constant?

This an M2 practice question that I can't wrap my head around. Any help or advice would be greatly appreciated.

Question

A car is travelling along a straight horizontal road against resistances to motion which are constant and total $200N$. When the engine of the car is working at a rate of $H$ kilowatts, the maximum speed of the car is $30\;ms^ {-1}$ .

a) Find the value of H.

I could do this bit and got the correct value of 72. No problems there.

The driver wishes to overtake another vehicle so she increases the rate of working of the engine by $20$% and this results in an initial acceleration of $0.32\;ms^{-2}$. Assuming that the resistances to motion remain constant,

b) Find the mass of the car.

For this section I understand to do $\frac{power}{speed} -2000 = m\times 0.32$, and I can work out the power as $72000$. However, I don't understand how I can assume that the speed is still $30 ms^{-1}$.

• Take a lookt at Physics Stack Exchange – Javi Jun 12 '18 at 19:50
• This is a physics question. It will be more suitable to ask it there. ^ – Bright Jun 12 '18 at 19:50
• Okay thank you! It didn't occur to me at all because it's part of my maths course but totally makes sense. – FlatWhiteVinyl Jun 12 '18 at 19:59

At the instant the power has increased it hasn't had a chance to accelerate the car, so the speed is the same. The problem assumes that the power increase is a step function. Once the power is increased, the speed will increase, increasing the work done by the resistance. The speed will now asymptotically approach $36 ms^{-1}$