Question

# A car accelerates uniformly from rest to 17.9 m/s in 6.31 s along a level stretch...

A car accelerates uniformly from rest to 17.9 m/s in 6.31 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 8.28 x 103 N, and (b) the weight of the car is 1.58 x 104 N.

Here, we have to find power required for two different cases in both cases we have given the weight of the car but other values like velocity and time are same. To calculate energy first we have to find kinetic energy and for kinetic energy, we need mass which is missing in question. Mass is calculated with the help of weight of the car.

Formula's used

1) Power (P)= Energy(E)/Time(t)

2) Energy(E)= 1/2*m*v^2 Where m= mass and v= velocity

3) Force(F)= m*g Where g= Gravitational constant (9.8)

Given

t= 6.31sec

v= 17.9 m/s

(a) Weight of car i.e. Force= 8.28*103N

F=mg

8.28*103=m*9.8

m= 87kg

Now energy

E=1/2m.v^2

E= 1/2*87*(17.9)^2= 13937.8J

Power, P= E/t

P=13937.8/6.31 = 2208.8W

(b )Weight of car i.e. Force= 1.58*104N

F=mg

1.58*104=m*9.8

m= 16.7kg

Now energy

E=1/2m.v^2

E= 1/2*16.7*(17.9)^2= 2675.4J

Power, P= E/t

P=2675.4/6.31 = 423.9W

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