Question

A runner started her race at rest and reached her maximum speed in 50 s. If she used 2000 N to reach that

maximum speed, what was her change in momentum from the beginning of the race to the moment she reached
maximum speed?

Answer 1

The change in momentum for the runner who applied a force of 2000 N over 50 seconds is 100,000 kg·m/s, calculated using the impulse-momentum theorem which states impulse equals force times time.

Step-by-step explanation:

The student's question asks about the change in momentum experienced by a runner who reaches her maximum speed with an applied force. To calculate the change in momentum, we use the impulse-momentum theorem, which states that the change in momentum (also known as impulse) is equal to the force applied times the time the force is applied. The formula for impulse (I) is I = F × t, where F is the force applied and t is the time the force was applied.

In this case, the runner applies a force of 2000 N over a time span of 50 seconds. Using the formula, we calculate the change in momentum as follows:

I = F × t

= 2000 N × 50 s

= 100,000 kg·m/s

Therefore, the runner's change in momentum from the start of the race to the moment she reached her maximum speed is 100,000 kg·m/s.

Answer 2

The change in momentum of the runner from the beginning of the race to the moment she reached her maximum speed is 100,000 N·s.

Step-by-step explanation:

The change in momentum of an object is given by the impulse imparted to it, which is the product of the force applied and the time for which it is applied. This is based on Newton's second law of motion, which states that the rate of change of momentum of a body is directly proportional to the force applied and occurs in the direction in which the force is applied.

In this case, the force applied is 2000 N and the time for which it is applied is 50 s. Therefore, the change in momentum can be calculated as follows:

Change in momentum = Force x Time

= 2000 N x 50 s

= 100,000 kg·m/s

So, the runner's change in momentum from the beginning of the race to the moment she reached maximum speed was 100,000 kg·m/s.