A 1000 kg car can accelerate from rest to v = 95 km/h in a time t = 7.4 s. (a) W

Question

A 1000 kg car can accelerate from rest to v = 95 km/h in a time t = 7.4 s.

(a) What is the average power delivered by the engine? Power = 47091.9

(b) If the power of the car is quadrupled, then the time it takes to reach the same speed will be equal to what fraction of t? t = 0.25

I need help with the last part:

If, instead the power of the car is smaller by a factor of 0.5 and the car accelerates for the same amount of time, by what factor will the maximum speed decrease? The answer isn't 0.3

Here's one of their practice problems to go by:

A 1000 kg car can accelerate from rest to v = 70 km/h in a time t = 7.4 s.

a) Power = 25500 W

b)  If the power of the car is tripled, then the time it takes to reach the same speed will be equal to what fraction of t? t = 0.333

c) If, instead the power of the car is smaller by a factor of 0.8 and the car accelerates for the same amount of time, by what factor will the maximum speed decrease? v = 0.894

Explanation / Answer

Vi = 0
Vf = 95 km/hr
= 95*1000 / 3600 m/s
= 26.39 m/s

Energy supplied by engine = 0.5*m*(Vf^2 - Vi^2)
= 0.5*1000*(26.39^2 - 0)
= 3.48187*10^5 J

A)
power = energy / time
= (3.48187*10^5) /7.4
= 47052 W

B)
If new power = 4* old power
= 4* 47052
= 188208 W
Energy will be same = 3.48187*10^5 J

power = energy / time
time will become 1/4 = 0.25

C)
P2 = 0.5*p1
t is same
so,
E2 = 0.5*E1
but E = 0.5*m*v^2
so,
V2^2 = 0.5*v1^2
V2 = 0.707 V1
Factor = 0.707

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