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Grade 12th passMechanics

The resistance to motion of an automobile depend on road friction which is almost independant of its speed v and on aerodynamic drag whic is propotional to v squareFor a particular 12000N car The total resistant Force F is given by F=300+1.8v^2 here F isin newton and v is in meter .Calculate the powerrequired from the motorto acccelerate the car at 0.92m persecond square when the speed is 80kmperhour.????

Profile image of Hamdia
7 Years agoGrade 12th pass
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1 Answer

Profile image of Arun
7 Years ago
This is relatively straightforward: To accelerate you need to overcome both the friction and air resistance, as well as provide force to change your velocity. So:
Ftotal = ma + 300 + 1.8v2.
First, convert v into m/s:
80 km/h = 80000 m/h = 22.22 m/s
And weight into mass: 12 000 N = mg
m = 1224 kg
 
Thus, F = 1224(.92) + 300 +1.8(22.22)2 = 2315 N. Finally, convert to horsepower:
1 Horsepower = 735.499 W
And 1 W = 1 Nm/s
So, we see that we’re missing one step here: the conversion from force to work and power. So, in one second the car will go:
D = v0 + .5at2 = 22.22 + .5(.92)(1) = 22.68 m.
 
The power is then: Fd/t = (2315 N)(22.68m)/1s = 52504 W
Which is 71.4 horsepower.