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Assume the aerodynamic drag force on a car is proportional to the speed. If the power output from the engine is doubled, then the maximum speed of the car. (A) is unchanged. (B) increases by a factor of (C) is also doubled. (D) increases by a factor of four.

Assume the aerodynamic drag force on a car is proportional to the speed. If the power output from the engine is doubled, then the maximum speed of the car.
(A) is unchanged.
(B) increases by a factor of
(C) is also doubled.
(D) increases by a factor of four.
 

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
The correct option is (B) increases by a factor of √2.
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. Thus option (B) is correct.

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