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A warehouse robot moves along a straight rail…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A warehouse robot moves along a straight rail. Its velocity is metres per second for seconds, where positive means towards the loading bay. The robot starts at rest at the first stop, and then it speeds up, slows, reverses and speeds up again. The controller records two different numbers. The first is how far the robot ends from its starting stop, which is the displacement. The second is the total length of rail its wheels travelled, which is the distance and which decides how soon the wheels wear. A technician also wants the average speed over the seven seconds, which is the distance divided by the time. Find the displacement, the distance and the average speed, and the two times at which the robot changes direction. Give each answer in metres or metres per second, to two decimal places where needed.
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The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. on .
Step 1. The turning times. at s and s. The velocity is positive on , negative on and positive on . So the robot changes direction at s and s.
Step 2. Values of . , , and .
Step 3. Displacement. m.
Step 4. Distance. The three pieces have sizes , and . The total is m.
Step 5. Average speed. m/s.
Answer: displacement m, distance m, average speed m/s, with turns at s and s.
Watch out. Dividing the displacement by s gives m/s. That is the mean velocity, not the average speed.
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