When a high-speed passenger train traveling at 161 km / h rounds a bend, the engineer is shocke

step 1 Okay, so we've got a high -speed passenger train traveling at 161 kilometers per hour. So V -Sub

When a high-speed passenger train traveling at 161 km / h...

When a high-speed passenger train traveling at $161 \mathrm{~km} / \mathrm{h}$ rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance $D=676 \mathrm{~m}$ ahead (Fig. 2-32). The locomotive is moving at $29.0 \mathrm{~km} / \mathrm{h}$. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided? (b) Assume that the engineer is at $x=0$ when, at $t=0$, he first spots the locomotive. Sketch $x(t)$ curves for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.

When a high-speed passenger train traveling at $161 \mathrm{~km} / \mathrm{h}$ rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance $D=676 \mathrm{~m}$ ahead (Fig. 2-32). The locomotive is moving at $29.0 \mathrm{~km} / \mathrm{h}$. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided?
(b) Assume that the engineer is at $x=0$ when, at $t=0$, he first spots the locomotive. Sketch $x(t)$ curves for the locomotive and high-speed train for the cases in which a collision is just avoided and is not quite avoided.

Key Concepts

Kinematic Equations

These equations describe the motion of an object under constant acceleration. They allow one to relate initial velocity, final velocity, acceleration, and displacement, which are crucial when calculating how much deceleration is needed to avoid a collision or how far an object travels before stopping.

Relative Motion

This concept involves analyzing the motion of objects with respect to each other, taking into account their individual speeds and positions. In collision avoidance problems, considering the relative speeds and distances between two objects helps determine the required deceleration or acceleration needed to prevent an impact.

Collision Avoidance

This involves determining the necessary adjustments in motion, such as braking or acceleration, to ensure that two moving objects do not collide. It requires careful calculation of distances, speeds, and deceleration rates to allow a safe clearance between objects moving on intersecting paths.

Time-Position Graphs

Drawing x(t) curves, or position versus time graphs, helps visualize and compare the trajectories of moving objects. This visual representation aids in understanding how the relative positions evolve over time, and it is particularly useful in analyzing scenarios where collision avoidance is required under different deceleration or acceleration conditions.

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