Final answer:
The runner's acceleration as they increase their velocity uniformly from 10.0 m/s to 25 m/s over 32 seconds is roughly 0.469 m/s².
Step-by-step explanation:
The question is asking to calculate the runner's acceleration during a uniform increase in velocity. Acceleration is defined as the change in velocity (Δv) over the change in time (Δt).
To find the acceleration, we use the formula:
a = Δv / Δt
Given that the initial velocity (vi) is 10.0 m/s and the final velocity (vf) is 25 m/s, with the time interval (Δt) being 32 s, we can calculate the change in velocity (Δv) as follows:
Δv = vf - vi = 25 m/s - 10 m/s = 15 m/s
Now, we can calculate the acceleration:
a = Δv / Δt = 15 m/s / 32 s = 0.46875 m/s²
Therefore, the runner's acceleration is approximately 0.469 m/s².