Additional Problems A red train traveling at 72 km / h and a green train traveling at 144 km / h

Additional Problems A red train traveling at 72 km / h and a...

Additional Problems A red train traveling at 72 $\mathrm{km} / \mathrm{h}$ and a green train traveling at 144 $\mathrm{km} / \mathrm{h}$ are headed toward each other along a straight, level track. When they are 950 $\mathrm{m}$ apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 $\mathrm{m} / \mathrm{s}^{2} .$ Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

Additional Problems
A red train traveling at 72 $\mathrm{km} / \mathrm{h}$ and a green train traveling at 144 $\mathrm{km} / \mathrm{h}$ are headed toward each other along a straight, level track. When they are 950 $\mathrm{m}$ apart, each engineer sees the other's train and applies the brakes. The brakes slow each train at the rate of 1.0 $\mathrm{m} / \mathrm{s}^{2} .$ Is there a collision? If so, answer yes and give the speed of the red train and the speed of the green train at impact, respectively. If not, answer no and give the separation between the trains when they stop.

Key Concepts

Stopping Distance Calculation

Stopping distance calculation employs kinematic equations to determine the distance an object travels from the moment braking begins until it comes to a complete stop. This calculation is crucial for safety analyses and determining whether two objects in motion will stop in time to avoid a collision.

Braking and Deceleration

Braking refers to the application of forces that reduce an object's speed, with deceleration being the term for negative acceleration during this process. Understanding how deceleration affects speed over time is critical when calculating the distance an object covers while slowing down.

Collision Prediction

Collision prediction uses the principles of kinematics and relative motion to assess whether two moving objects on converging paths will meet. By comparing their stopping distances and the initial separation between them, one can predict if and when a collision will occur.

Kinematics under Constant Acceleration

This concept involves analyzing the motion of objects when they experience a constant acceleration or deceleration. It uses equations that relate displacement, velocity, acceleration, and time, which are essential for calculating how far an object travels or how its speed changes over time under uniform acceleration conditions.

Relative Motion

Relative motion studies the movement of objects with respect to one another. When two objects are moving toward each other, their speeds and decelerations need to be combined to assess the effective closing speed and determine outcomes such as collision or safe stopping distance.

Transcript

00:01 Here we're going to find the stopping distance of the red train first because that is the slower train.

00:05 It's going to take much less, it's going to stop at a shorter distance to stop the red train, of course, because it's moving slower initially.

00:13 So we can say that delta x of the red train would be equal to velocity of the red train final squared minus velocity of the red train initial squared divided by 2 times a.

00:28 We know that we're trying to stop so this term goes to zero and this is equaling essentially negative v subred initial squared divided by two times a we're gonna say that v of the red train initially we know this to be equal to 72 kilometers and we're gonna say that this is approximately 20 meters per second so this would be equal to negative 20 meters per second squared divided by 2 times negative 1 meters per second squared and we find that the change in displacement in the x direction of the ray train would be approximately equal to 200 meters so the red train will come to a stop at 200 meters and so now we can then find the speed of the other train at that location.

01:27 So we can say that v final, or there we can say v green final squared would be equal to v green initial squared.

01:38 We'll say plus 2a delta x.

01:42 Now here we know that v green initial is equalling.

01:47 If we chose the initially the initial velocity of the red train to be positive and the green train is moving towards the red train.

01:57 This means that the initial velocity of the green train is negative...

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