An electric racecar uses a 7000motor that operates is two regimes: from 0-20m/s

Question

An electric racecar uses a 7000motor that operates is two regimes: from 0-20m/s it produces constant torque that provides 10m/s2 of forward acceleration, from 20-30m/s it produces a constant power and hence a hyperbolically decreasing torque and acceleration. The equation for acceleration from 20-30m/s is: a=P/(v*m) where P is power, v is vehicle speed and m is vehicle mass. If P=70kW and m is 350kg, how long does it take the vehicle to accelerate from rest to 30m/s? How far did it travel in this time?

I found solutions to questions similar to this, but they seem wrong or don't give complete explanations. The part of the question that has to do with the non-constant acceleration is what I'm confused about. Thank you!

Explanation / Answer

Applying formula -

v = u + at

S = ut + 1/2at2

long does it take the vehicle to accelerate =   20/10 + (30 - 20)/20

                                                                  = 2.5 sec

far did it travel in this time =   1/2 * 20 * 2.52

                                           = 62.5 m

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