Question

Assume the aerodynamic drag force force on a car is proportional to its speed if the power output is doubled find maximum speed

Answer 1

In accordance to question, the aerodynamic drag force (F) on a car is proportional to speed (v).

So, F v

So, F= kv …… (1)

Where, k is a constant.

From equation (1), speed will be,

v = F/k …… (2)

Since force acting on the body (F) is equal to the power delivered (P) to the body divided by speed of the body (v).

So, F = P/v …… (3)

Putting the value of equation (3) in equation (2) we get,

v = F/k
= P/v /k
= P/vk

So, v2 = P/k

Or, v = √P/k …… (4)

If the power output (Pʹ = 2P) from the engine is doubled, then the maximum speed (vʹ) of the car will be,

vʹ = √Pʹ/k
=√2P/k (Since, Pʹ = 2P)
= √2 (√P/k)
= √2 v (Since, v = √P/k) …… (5)

From equation (5) we observed that, if the power output from the engine is doubled, then the maximum speed of the car will be, increased by a factor of √2.