Final answer:
To calculate the distance traveled by a microorganism while decelerating, we use motion equations with given initial and final speeds, time, and derived acceleration. After computing the deceleration, the distance is found to be 112.5 μm.
Step-by-step explanation:
To calculate the total distance traveled by a microorganism while stopping, we can use the equations of motion under constant acceleration (in this case, negative acceleration or deceleration). The initial speed (vi) of the microorganism is 150 μm/s. It slows down to a final speed (vf) of 75 μm/s in a given time (t) of 1.5 ms (or 1.5 × 10−6 s).
The deceleration (a) can be found using the formula: a = (vf - vi) / t.
After calculating the deceleration, we can find the distance (d) using the formula: d = vi × t + 0.5 × a × t2.
Lets plug in the values:
- vi = 150 μm/s
- vf = 75 μm/s
- t = 1.5 ms = 1.5 × 10−3 s
First, we find the deceleration:
a = (75 μm/s - 150 μm/s) / (1.5 × 10−3 s) = -50,000 μm/s2
Now we calculate the distance:
d = (150 μm/s × 1.5 × 10−3 s) + 0.5 × (-50,000 μm/s2) × (1.5 × 10−3 s)2 = 112.5 μm.