You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at 88 km/h collided with a slower train traveling in the same direction at 22 km/h . Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at 2.2 m/s2 when it was 42 m from the slower train, while the slower train continued at constant speed. What do you report?

Question

You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at 88 km/h collided with a slower train traveling in the same direction at 22 km/h . Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at 2.2 m/s2 when it was 42 m from the slower train, while the slower train continued at constant speed. What do you report?

Answer 1

To determine the relative speed of the collision, we can use the information provided. Here are the steps to calculate it:

1. Convert the speeds of the trains to meters per second (m/s) to match the units used for acceleration.

Speed of the faster train = 88 km/h
Converting km/h to m/s: (88 km/h) * (1000 m/1 km) * (1 h/3600 s) = 24.44 m/s

Speed of the slower train = 22 km/h
Converting km/h to m/s: (22 km/h) * (1000 m/1 km) * (1 h/3600 s) = 6.11 m/s

2. Calculate the time it took for the faster train to reach the slower train.

In order to find the time, we need to determine the distance the faster train traveled before the collision.

Distance traveled by the faster train = initial distance - distance at the time of acceleration
= 42 m - 0 m (because the faster train hasn't moved yet)
= 42 m

Using the equation of motion: distance = initial velocity * time + (1/2) * acceleration * time^2, we can solve for time.

distance = 42 m
initial velocity = 24.44 m/s (because the faster train is initially moving at this speed)
acceleration = -2.2 m/s^2 (because the train is negatively accelerating)
time = ?

Rearranging the equation to solve for time:
time = (-initial velocity ± √(initial velocity^2 - 4 * (1/2) * acceleration * distance)) / (2 * (1/2) * acceleration)

time = (-24.44 ± √(24.44^2 - 4 * (-2.2) * 42)) / (2 * (-2.2))

By solving this equation, we can find the time it took for the faster train to reach the slower train.

3. Calculate the relative speed of the collision.

The relative speed of the collision is the difference between the speeds of the two trains.

Relative speed = speed of the faster train - speed of the slower train

By substituting the calculated values for the speeds, you can find the relative speed of the collision.

Therefore, based on the information provided, you would need to follow these steps to determine the relative speed of the collision.