Locomotive exert on a 13160-kg boxcar to make it accelerate forward at 0.40 m/s2. How long will it take the boxcar to reach its cruising speed of 105 km/h (65.2 mph or 29.2 m/s)?
29.2m/s= t*.40m/s^2+0
t=29.2m/s/.40m/s^2
t=73s
To solve this problem, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net Force = Mass × Acceleration
We know the mass of the boxcar is 13,160 kg, and the acceleration is 0.40 m/s^2. Therefore, we can calculate the net force:
Net Force = 13,160 kg × 0.40 m/s^2 = 5,264 N
Now, we need to consider the force exerted by the locomotive. Let's assume that the force exerted by the locomotive is constant throughout the acceleration. Therefore, the net force acting on the boxcar will be equal to the force exerted by the locomotive:
Net Force = Force Locomotive
Now, we can rearrange the formula to solve for time:
Time = (Final Velocity - Initial Velocity) / Acceleration
We need to convert the cruising speed of the boxcar from km/h to m/s:
Final Velocity = 105 km/h × (1000 m/1 km) × (1 h/3600 s) = 29.2 m/s
Initial Velocity is 0 m/s since the boxcar starts from rest.
Plugging in the values in the formula:
Time = (29.2 m/s - 0 m/s) / 0.40 m/s^2
Time = 73 seconds
Therefore, it will take the boxcar 73 seconds to reach its cruising speed of 105 km/h.