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Bill and Tom are both towing wagons. Bill's wagon weighs 10 pounds, and Tom's wagon weighs 20 pounds. Bill is pulling his wagon with twice the force that Tom is. How do the wagon speeds compare? A) Both wagons will be moving at the same speed. B) Bill's wagon is moving 4 times faster than Tom's. C) Tom's wagon is moving 4 times faster than Bill's. D) Bill's wagon is moving 2 times faster than Tom's.

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Answer:

  • B) Bill's wagon is moving 4 times faster than Tom's.

Explanation:

The motion of the wagons is determined by the net force that acts upon them, according to Newton's second law of motion:

  • Force = mass × acceleration ⇒ acceleration = Force / mass

From your data, you can fill this table to compare the accelerations:

                          Bill's wagon   Tom's wagon

mass (lb)                 10                      20

force                       2F                      F

acceleration           2F/10                 F/20

Find the ratio between both accelarations:

  • Bill's wagon acceleration / Tom's wagon acceleration
  • (2F/10) / (F/20) = (2 × 20 / 10 ) = 4

Meaning that the acceleration of Bill's wagon is 4 times the acceleration of Tom's wagon.

Assuming, that both wagons start from rest, you can obtain the speeds from the kinematic equation for uniformly accelerated motion:

  • Speed = acceleration × time, V = a × t.

Call the acceleration of Tom's wagon X, then the acceleration of Bill's wagon will be 4X.

So, depending on the time, using V = a × t, the speeds will vary:

t (s)                                      1         2         3        4

Speed Tom's wagon         X        2X      3X     4X  

Speed Bill's wagon           4X      8X     12X    16X

Concluding that Bill's wagon is moving 4 times faster than Tom's (option B).

Answer:

B

Explanation:

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