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

Answer 1

The acceleration of the microorganism is approximately -57,692 μm/s². The negative sign indicates deceleration or a decrease in speed.

Step-by-step explanation:

To find the acceleration of the microorganism, you can use the formula for acceleration:

`\[ a = (\Delta v)/(\Delta t) \]`

where:

a is the acceleration,

`\( \Delta v \)` is the change in velocity,

`\( \Delta t \)` is the change in time.

In this case, the microorganism's speed drops from 150 μm/s to 75 μm/s, so
`\( \Delta v \)` = 75 μm/s - 150 μm/s = -75 μm/s. The negative sign indicates a decrease in speed.

The time interval is given as
`\( \Delta t = 1.3 \, \text{ms} \)`, but it needs to be converted to seconds by dividing by 1000:

`\[ \Delta t = 1.3 \, \text{ms} * \frac{1 \, \text{s}}{1000 \, \text{ms}} = 0.0013 \, \text{s} \]`

Now, substitute these values into the formula:

`\[ a = (-75 \,)/(0.0013 \, ) \]` μm/s²

Calculate the acceleration:

`\[ a \approx -57,692 \, \]` μm/s²

So, the acceleration of the microorganism is approximately -57,692 μm/s². The negative sign indicates deceleration or a decrease in speed.