Question

Resistance to the motion of an automobile consists of road friction, which is almost independent of speed, and air drag, which is proportional to speed-squared. For a certain car with a weight of 12000 N, the total resistant force F is given by F = 300 + 1.8v2, with F in newtons and v in meters per second. Calculate the power (in horsepower) required to accelerate the car at 0.96 m/s^2 when the speed is 82 km/h.

Answer 1

73.52983 Hp

Step-by-step explanation:

m = Mass of car =
`(W)/(g)`

W = Weight of car = 12000 N

a = Acceleration = 0.96 m/s²

Velocity of the car

`v=82* (1000)/(3600)\\\Rightarrow v=(82)/(3.6)\\\Rightarrow v=(41)/(1.8)`

From the question

`F=300+1.8v^2\\\Rightarrow F=300+1.8* \left((41)/(1.8)\right)^2\\\Rightarrow F=1233.88\ N`

Balancing the forces

`(P)/(v)-1233.88=ma\\\Rightarrow P=(ma+12000)v\\\Rightarrow P=\left((12000)/(9.81)* 0.96+1233.88\right)(41)/(1.8)\\\Rightarrow P=54853.26055\ W=(54853.26055)/(746)\\\Rightarrow P=73.52983\ Hp`

The power is 73.52983 Hp