A train travels 84 km/h when it reaches a slower train 47 meters ahead traveling the same direction at 24 km/h. If the faster train decelerates at 2.1 m/s^2 while the slower train is at a constant speed, when will they collide? If the train that is faster begins to decelerate at 2.1 m/s^2 while the slower train continues at a constant speed, what willbe the relative speed in which they will collide?

Question

A train travels 84 km/h when it reaches a slower train 47 meters ahead traveling the same direction at 24 km/h. If the faster train decelerates at 2.1 m/s^2 while the slower train is at a constant speed, when will they collide? If the train that is faster begins to decelerate at 2.1 m/s^2 while the slower train continues at a constant speed, what willbe the relative speed in which they will collide?

I got 4.9 seconds for the first one and I do not get the last one. Thanks Y'all.

Answer 1

To find out when the two trains will collide, you can use the concept of relative motion. Here's how you can calculate it step by step:

1. Convert the speeds of the trains to meters per second (m/s):
- Faster train speed = 84 km/h = (84 * 1000) / 3600 = 23.33 m/s
- Slower train speed = 24 km/h = (24 * 1000) / 3600 = 6.67 m/s

2. Determine the relative velocity between the trains by subtracting the slower train's speed from the faster train's speed:
- Relative velocity = faster train speed - slower train speed
= 23.33 m/s - 6.67 m/s
= 16.66 m/s

3. Calculate the time it will take for the faster train to reach the slower train:
- Use the equation: Distance = Initial velocity * Time + 0.5 * Acceleration * Time^2
- Rearrange the equation to solve for Time:
Time = (Final velocity - Initial velocity) / Acceleration
Here, the final velocity is 0 since the faster train comes to a stop when it collides with the slower train.
- Substituting the known values:
Time = (0 - 23.33) / (-2.1)
= 11.1 seconds (approximately)

So, the two trains will collide after approximately 11.1 seconds.

Now, let's calculate the relative speed at the time of collision if only the faster train decelerates:

1. The relative speed can be calculated by subtracting the slower train's speed from the faster train's speed at the time of collision:
- Relative speed = faster train speed - slower train speed
= 0 m/s - 6.67 m/s
= -6.67 m/s

The negative sign indicates that the two trains collide while moving in opposite directions. Therefore, the relative speed at the time of collision, when only the faster train is decelerating, is 6.67 m/s in the opposite direction of the slower train's motion.

I hope this explanation helps clarify the solution to your problems. Let me know if you have any further questions!