Question

A microorganism swimming through water at a speed of 150 μm/s suddenly stops swimming. its speed drops to 75 μm/s in 1.3 ms .what is the total distance in μm it travels while stopping?

Answer 1

The total distance traveled while stopping is 112.5 μm. The microorganism's average speed during deceleration is 112.5 μm/s. Using the formula
`\( \text{Distance} = \text{Average Speed} * \text{Time} \),` with a deceleration time of 1.3 ms, the total distance covered is 112.5 μm. This calculation reveals the distance traveled during the microorganism's stopping phase.

Step-by-step explanation:

The initial speed of the microorganism is 150 μm/s, and it comes to a stop in 1.3 ms (milliseconds), during which its speed decreases to 75 μm/s. To find the total distance traveled while stopping, we can use the average speed formula:

`\[ \text{Average Speed} = \frac{\text{Initial Speed} + \text{Final Speed}}{2} \]`

The average speed during the deceleration is

`\( (150 \ μm/s + 75 \ μm/s)/(2) = 112.5 \ μm/s \).`

Now, we can use the formula

`\( \text{Distance} = \text{Speed} * \text{Time} \)`

to find the distance traveled:

`\[ \text{Distance} = \text{Average Speed} * \text{Time} \]`

Convert the time from milliseconds to seconds (1.3 ms = 0.0013 s) and substitute the values:

`\[ \text{Distance} = 112.5 \ μm/s * 0.0013 \ s = 0.14625 \ μm \]`

So, the microorganism travels a total distance of 112.5 μm while coming to a stop.

In conclusion, the average speed during deceleration is crucial for determining the distance covered. By applying the average speed formula and converting the time to seconds, we find that the microorganism travels 112.5 μm while stopping. This calculation helps in understanding the motion dynamics and provides insight into the distance covered during the deceleration process.