Final answer:
To find the time for a train to accelerate to 70.0 km/h, we converted the speed to m/s, calculated the acceleration using Newton's second law, and used the kinematic equation to find the time, which is approximately 286 seconds.
Step-by-step explanation:
To calculate how much time it takes for the train to increase its speed from rest to 70.0 km/h under a constant force, we start by converting the final speed to meters per second, then use the formula derived from Newton's second law, F = ma, to find the acceleration, and finally use the kinematic equation v = at to find the time.
First, convert 70.0 km/h to meters per second:
- 70 km/h = (70 × 1000 m/km) / (3600 s/h) = 19.44 m/s
Next, calculate the acceleration a:
- a = F/m = (6.80 × 10⁵ N) / (1.00 × 10⁷ kg) = 0.068 m/s²
Finally, calculate the time t using v = at:
- t = v / a = 19.44 m/s / 0.068 m/s²
- t = 286 seconds
Therefore, it would take the train approximately 286 seconds to reach a speed of 70.0 km/h from rest.