1. Acceleration is defined as the time rate of change of velocity;

Question

that is,[latex]a=\frac{ ext { change in } v}{ ext { time }}[/latex]. Are we now saying that acceleration is instead the ratio of force to mass—that is,[latex]a=\frac{F}{m}[/latex]? Which is it?

2. A jumbo jet cruises at constant velocity of 1000 km/h when the thrusting force of its engines is a constant 100,000 N. What is the acceleration of the jet? What is the force of air resistance on the jet?

3. Suppose you apply the same amount of force to two separate carts, one cart with a mass of 1 kg, and the other with a mass of 2 kg. Which cart will accelerate more, and how much greater will the acceleration be?

Accepted Answer

1. Both. Acceleration is defined as the time rate of change of velocity and is produced by a force. How much force/mass (usually the cause) determines the rate change in velocity/time (usually the effect). So we must first define acceleration and then define the terms that produce acceleration.

2. The acceleration is zero, as evidenced by the constant velocity. Because the acceleration is zero, it follows from Newton’s second law that the net force is zero, which means that the force of air resistance must just equal the thrusting force of 100,000 N and act in the opposite direction. So the air resistance on the jet is 100,000 N. This is in accord with [latex]\Sigma F=0[/latex]. (Note that we don’t need to know the velocity of the jet to answer this question, but only that it is constant—our clue that acceleration, and therefore net force, is zero.)

3. The 1-kg cart will have more acceleration—twice as much, in fact—because it has half as much mass—which means half as much resistance to a change in motion.

Question 3.S&C.2: 1. Acceleration is defined as the time rate of change of vel...

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