Question

When studying the motion of an object, we can analyze it using kinematic equations or energy equations. Both types of equations give information about position and velocity. Kinematic equations give information about the motion of an object from moment to moment, while energy equations typically detail the initial and final points of the motion. Consider a car traveling at 6 m/s. When the driver breaks the car travels 18 meters before coming to a stop. (This is one question, just multiple parts)

If the initial speed of this car doubles, the distance required to stop this car:
(a) None of these
(b) Increases by a factor of √2
(c) Remains the same
(d) Increases by a factor of 4
(e) Increases by a factor of 2

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If the mass of the car doubles but the initial speed remains the same, the distance required to stop the car:
(a) Remains the same
(b) None of these
(c) Increases by a factor of √2
(d) Increases by a factor of 4
(e) Increases by a factor of 2

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What work is being done on a car moving with a constant speed along a straight, level road?
I. No work of any kind
II. Work is being done on the car
III. Work is being done by the car

(a) III only
(b) II only
(c) II and III only
(d) I, II, and III
(e) I only

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Chemical potential energy stored in gasoline is converted to kinetic energy as the car increases its speed from 0 m/s to 10 m/s. Then the car accelerates from 10 m/s to 20 m/s. The energy required to go from 10 m/s to 20 m/s, compared to the energy required to go from 0 m/s to 10 m/s is:
(a) Three times as much
(b) The same
(c) None of these
(d) Two times as much
(e) Half as much

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Two cars traveling on a level road have the same kinetic energy. Car 1 has twice the mass of Car 2. Compare the speeds of the two cars, v1 and v2, and the work required to stop each car, W1 and W2.
(a) v1 is v2⁄4; W1 is same as W2
(b) None of these
(c) v1 is half v2; W1 is twice W2
(d) v1 is v2⁄√2; W1 is same as W2
(e) v1 is twice v2; W1 is twice W2

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For the car described in the passage, what is the magnitude of its acceleration as it comes to a stop? ______

Answer 1

From kinematic equation of motion

v^2 = v₀^2 + 2a(x - x0)

Here, Where v =0 (final speed) and 2(x - x0) is constant (stopping distance), so:

v₀^2 = ka ; here k is constnat

stopping distance linearly varies with Initial speed.

If you double v₀, you get 2^2 ka=4ka

From Newton's second law, force F = ma,

As acceleration in the above case incrased by 4 times, the required force should incrased by 4 times.

Correct option is (d)

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If the mass doubles, the kinetic energy will double, but that the friction stopping force will also double. It implies that, the stopping distance is independent of the mass (or weight) of the car.

Correct option is (a)

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As car moving at constnat speed in a straight line path, its acceleartion is zero. Thus, the work done is zero.

W = F.s = ma. s ( here a = 0 implies that Work done W = 0 )

Correct option is (e)