Free Answer 2. Version B A new green TriMet bus running the #2 bus line in Portland, Oregon pulls out from a bus-stop accelerating at a constant rate from rest for 12 seconds at ₁ in the positive x direction. Once it reaches cruising speed after accelerating from rest, the green bus continues down the straight road at constant velocity for 25 seconds. To stop at the next bus-stop, the driver then slows the bus down at a constant rate of acceleration à2 coming to a stop shortly afterwards. We want to determine the total distance traveled by the green bus and the average speed of the bus if we know a₁ and a2.
Free Answer 2. Version B A new green TriMet bus running the #2 bus line in Portland, Oregon pulls out from a bus-stop accelerating at a constant rate from rest for 12 seconds at ₁ in the positive x direction. Once it reaches cruising speed after accelerating from rest, the green bus continues down the straight road at constant velocity for 25 seconds. To stop at the next bus-stop, the driver then slows the bus down at a constant rate of acceleration à2 coming to a stop shortly afterwards. We want to determine the total distance traveled by the green bus and the average speed of the bus if we know a₁ and a2.
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Transcribed Image Text:**Free Answer 2. Version B**
A new green TriMet bus running the #2 bus line in Portland, Oregon, pulls out from a bus-stop accelerating at a constant rate from rest for 12 seconds at \(\vec{a}_1\) in the positive x direction. Once it reaches cruising speed after accelerating from rest, the green bus continues down the straight road at constant velocity for 25 seconds. To stop at the next bus-stop, the driver then slows the bus down at a constant rate of acceleration \(\vec{a}_2\) coming to a stop shortly afterwards.
We want to determine the total distance traveled by the green bus and the average speed of the bus if we know \(\vec{a}_1\) and \(\vec{a}_2\).
(A) **Sketch a graph of velocity versus time for this short trip.** Label the time axis to indicate which portions of the curve(s) correspond to the above intervals. Identify and write knowns and unknowns.
(B) Without using numerical values, determine which physics equations of motion will help solve this problem. Simplify as useful for this particular case.
(C) If \(\vec{a}_1 = 1.5 \, \text{m/s}^2\) and \(\vec{a}_2 = -2.5 \, \text{m/s}^2\) determine the total distance traveled during all intervals. Then determine the average velocity of the bus during the entire trip.
Expert Solution
Step 1
Solution:
In the first half of the motion, acceleration is constant. The motion is an accelerated motion. The slope of the velocity time graph gives the acceleration. Since acceleration is the constant slope is also the same. Now in the nest half of the motion, velocity is constant and acceleration is zero. Therefore, the slope will also be zero. Now after 25s brake is applied which means velocity will decrease and negating acceleration is working. The velocity-time graph of the motion is shown below:
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