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Question 3.WE.6: The maximum forward force a car can provide is 500 N. The ai...

The maximum forward force a car can provide is 500 N. The air resistance F which the car experiences depends on its speed according to F = 0.2 v², where v is the speed in ms^{−1}. Determine the top speed of the car.

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Step 1 From the equation F = 0.2 v², you can see that the air resistance increases as the car goes faster. Top speed is reached when the forward force equals the air resistance. So, at top speed:
500 = 0.2 v²
Step 2 Rearranging gives:

v² = \frac{500}{0.2} = 2500

 

v = 50  m  s^{-1}

So the car’s top speed is 50  m  s^{-1} (this is about 180  km  h^{-1})

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