Final answer:
The force propelling a 97,000 kg locomotive from rest to 22.35 m/s in 5.0 seconds is calculated using Newton's second law (F = ma) to be 433,590 Newtons.
Step-by-step explanation:
The force that propels a 97,000 kg locomotive from rest to 22.35 m/s in 5.0 s can be calculated using Newton's second law of motion, which states that force (F) is the product of an object's mass (m) and its acceleration (a). The acceleration can be determined by the change in velocity (Δv) over the time (t) it takes for the change to occur, a = Δv/t. In this case:
- Change in velocity (Δv) is 22.35 m/s (final velocity) - 0 m/s (initial velocity) = 22.35 m/s.
- Time (t) is 5.0 s.
Therefore, the acceleration (a) is 22.35 m/s / 5.0 s = 4.47 m/s².
Now, using the formula F = ma:
- Mass (m) is 97,000 kg.
- Acceleration (a) is 4.47 m/s².
The force (F) is therefore 97,000 kg * 4.47 m/s² = 433,590 N. So the force that propels the locomotive down the track is 433,590 Newtons.