Twenty students ride a school bus that has a mass of 2500 kg and moves with a speed of 4.25 m/s. The driver has a mass of 75 kg. What is the magnitude of the momentum of the bus and it's passengers if the average mass of each student is 125 kg?  If 8 students get off from the bus, what must be the speed of the bus to maintain its original momentum?

Expert Answers

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Momentum is a product of an objects mass times the velocity it is experiencing.  Momentum may be increased or decreased by manipulation of either the mass or the velocity.  The formula for determining momentum is:  P = mv, where P would be the momentum of the object, m is the mass of the object, and v is the velocity of the object.  The total mass you have listed is as follows:

2500 kg (bus) + 75 kg (driver) + 2500 kg (students) = 5075 kg

Substituting into the formula: 

P = 4.25 m/s  x  5075 kg

P= 21,568.75 kg m/s

As I mentioned, since there are two factors that determine momentum, we can still have the same momentum if we change the numbers around.  If we subtract eight of the twenty students, the mass would change by 1000 kg.

8 x 125 kg = 1000 kg

Subtract 1000 kg from the initial mass, 5075 kg, and you get 4075 kg.

To maintain the same number on momentum, we would have to increase the number for velocity.  We could find that value by doing the following:

21,568.75 kg m/s  =  (v) (4075 kg)

Divide both sides by 4075 kg, and we discover what the new velocity would have to be:

21,568 kg m/s /4075 kg  =  (v) (4075 kg) /4075 kg

5.29 m/s  =  (v)

The new velocity would have to be 5.29 m/s.

It should also be pointed out, you have listed speed, which is helpful in determining momentum, but speed in and of itself is not velocity.  In velocity, there is a directional component, such as "5.29 m/s, South."

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