a) On the Acme W&W company production line, parts have to be transported 100 m by conveyor belt to a machine area. The parts move at a constant speed of 2.5 m/s. How much time does it take to move a part 100 m?
On the same conveyor belt as described in problem a), the part must slow down to 0.2 m/s over a distance of 0.9 m once it reaches the machine area. The original speed was 2.5 m/s. What is the average acceleration while slowing down? How much time does it take to slow down?
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a) To calculate the time it takes for a part to move 100 m at a constant speed of 2.5 m/s, we can use the formula:
Time = Distance / Speed
In this case, the distance is 100 m and the speed is 2.5 m/s.
Time = 100 m / 2.5 m/s
Simplifying the equation, we have:
Time = 40 s
So, it takes 40 seconds to move a part 100 m at a constant speed of 2.5 m/s.
b) To find the average acceleration while slowing down, we need to use the formula for acceleration:
Acceleration = Change in Speed / Time
In this case, the change in speed is from 2.5 m/s to 0.2 m/s, and the distance over which this change occurs is 0.9 m.
Change in Speed = Final Speed - Initial Speed
Change in Speed = 0.2 m/s - 2.5 m/s
Change in Speed = -2.3 m/s
Acceleration = -2.3 m/s / Time
We need to find the time it takes to slow down the part. To find the time, we can use the formula:
Time = Distance / Speed
In this case, the distance is 0.9 m and the speed is 2.5 m/s.
Time = 0.9 m / 2.5 m/s
Simplifying the equation, we have:
Time = 0.36 s
Now, substituting the value of time into the acceleration formula:
Acceleration = -2.3 m/s / 0.36 s
Simplifying the equation, we have:
Acceleration ≈ -6.39 m/s²
So, the average acceleration while slowing down is approximately -6.39 m/s².
The time it takes to slow down is 0.36 seconds.