Running into the train at that speed would severely damage both train and passengers. Calculate the minimum time Superman must take to stop the train, if the passengers experience an average horizontal force of 0.520 their own weight.
and
How far does the train then travel while being slowed to a stop?
acceleration = -.520(9.8) = -5.1 m/s^2
initial speed Vo = 65 km/hr(1hr/3600s)(1000 m/km)=18 m/s
From your physics text for constant acceleration
v = Vo + a t
here we have our initial Vo is 18 and we stop, v = 0
0 = 18 - 5.1 t
so t = 18/5.1 = 3.53 seconds
i have one more
How far does the train then travel while being slowed to a stop?
d = Vo t + (1/2) a t^2
d = 18 * 3.53 - (5.1/2)(3.53)^2
By the way, if you are really used to these problems you would just use the average speed during deacceleration (18/2 = 9 m/s) times the time (3.53 s)
Well, let's begin by acknowledging that Superman is pretty super. I mean, he's faster than a speeding bullet, right? So let's assume he can stop the train in the blink of an eye.
But hey, we don't want him to pull a muscle or damage his suit while doing so, so let's be a bit more realistic. To make it a smooth stop, Superman should take at least a few seconds (or maybe a superheroic fraction of a second) to halt the train. It's all about safety first!
As for how far the train travels while being slowed to a stop, well, that depends on how fast it was going initially and how quickly Superman can put on the brakes. Without those details, it's hard for me to come up with a specific answer.
But don't worry, Superman always knows how to save the day!
To calculate the minimum time Superman must take to stop the train, we need to know the mass of the train and the deceleration required. Similarly, to determine how far the train travels while being slowed to a stop, we need to know the initial velocity of the train and the time taken to stop. Unfortunately, these details are not provided in your question.
However, I can provide you with a general explanation of how to approach these calculations if you have the necessary information.
1. Minimum time to stop the train: To calculate the minimum time Superman needs to stop the train, you would need to know the mass of the train and the desired deceleration.
- Determine the mass of the train in kilograms (kg).
- Calculate the deceleration required by multiplying the average horizontal force experienced by the passengers by the gravitational acceleration (g = 9.8 m/s²). This gives you the deceleration in m/s².
- Then, use the equation of motion: acceleration = change in velocity / time (a = Δv / t) to solve for time (t). Rearrange the equation to solve for time: t = Δv / a, where Δv is the change in velocity (initial velocity - final velocity) and a is the deceleration.
2. Distance traveled while being slowed to a stop: To determine how far the train travels while being slowed to a stop, you would need to know the initial velocity and the time taken to stop.
- Find the initial velocity of the train in meters per second (m/s).
- Use the formula for distance traveled during uniform acceleration: distance = (initial velocity × time) + (0.5 × acceleration × time²). Since the train is slowing down, the acceleration would be negative, opposite in direction to the motion.
Please provide the missing information, and I will be happy to assist you in calculating the minimum time required by Superman to stop the train and the distance the train travels while being slowed to a stop.