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Two cars are at a stop light. When the light turns green the car of mass begins to move with acceleration a; the car of mass 2m moves in the same direction with acceleration a/2. Which car engine delivers the most power? (A) The car of mass m (B) The car of mass 2m (C) The power is the same for both cars.

Two cars are at a stop light. When the light turns green the car of mass begins to move with acceleration a; the car of mass 2m moves in the same direction with acceleration a/2. Which car engine delivers the most power?
(A) The car of mass m
(B) The car of mass 2m
(C) The power is the same for both cars.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
The correct option is (C) the power is the same for both cars.
Power delivered (P) to the body is equal to the force acting on the body (F) times speed of the body (v).
So, P = Fv …… (1)
Again we know that, force acting on the particle (F) is equal to the mass of the particle (m) times acceleration of the particle (a).
F = ma …… (2)
Putting the value of equation (2) in equation (1), the power will be,
P = Fv
= mav …… (3)
To obtain power (P) of the first car, substitute m for mass m and a for acceleration a in the equation P = mav,
P = mav ……(4)
To obtain power (P) of the second car, substitute 2m for mass m and a/2 for acceleration a in the equation P = mav,
P = (2m) (a/2) v
= mav ……(5)
From equation (4) and equation (5) we observed that, both the car engine delivers equal amount of power. Thus option (C) is correct.

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