Two subway stops are separated by 1100 m. If a subway train accelerates at +1.2 m / s^2 from r

step 1 In this problem of motion along a straight line we have given that. 2 subway stops are separated

Two subway stops are separated by 1100 m. If a subway train...

Two subway stops are separated by $1100 \mathrm{~m}$. If a subway train accelerates at $+1.2 \mathrm{~m} / \mathrm{s}^{2}$ from rest through the first hall of the distance and decelerates at $-1.2 \mathrm{~m} / \mathrm{s}^{2}$ through the second half, what are (a) its travel time and (b) its maximum speed? (c) Graph $x, v$ and $a$ versus $t$ for the trip.

Key Concepts

Constant Acceleration Kinematics

This concept involves using the equations of motion that relate displacement, time, acceleration, and velocity for objects undergoing uniform acceleration. It includes formulas such as displacement = ½·acceleration·time² and final velocity = acceleration·time, which are used to calculate distances traveled during constant acceleration or deceleration, as well as maximum speeds reached during motion.

Symmetric Acceleration-Deceleration Motion

This concept describes a motion scenario where a vehicle or object accelerates uniformly to a midpoint and then decelerates uniformly with the same magnitude of acceleration in the opposite direction until it comes to rest. The symmetry implies that the time taken to accelerate is equal to the time taken to decelerate and that the distance covered during acceleration is equal to the distance covered during deceleration, which simplifies the analysis of the overall motion.

Graphical Representation of Motion

This concept pertains to depicting the relationships between displacement, velocity, and acceleration as functions of time. Graphs are used to visually interpret the behavior of moving objects. For example, an x versus t graph shows how position changes over time, a v versus t graph illustrates the changes in speed and indicates acceleration regions, and an a versus t graph directly reflects the constant rates of acceleration and deceleration.

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