A sprinter runs 100.0 m in 12.2 seconds. If he travels at constant acceleration for the first 50.0 m and then at constant velocity for the final 50.0 m, what was his peak speed?
A) 12.3 m/s
B) 17.5 m/s
C) 8.20 m/s
D) 4.10 m/s

Question

Quizplus · Accepted Answer

The sprinter's peak speed can be found by calculating the time taken to cover the first 50.0 m under constant acceleration and then using the remaining time to cover the second 50.0 m at constant velocity. The total distance $d$ covered under constant acceleration can be expressed using the equation $d = \frac{1}{2}at^2$, where $a$ is the acceleration and $t$ is the time. Since the sprinter covers the first 50.0 m under constant acceleration, we can set $d = 50.0 m$. However, without the explicit time $t$ for the first 50.0 m, we directly calculate the average velocity for the entire 100.0 m, which is $v = \frac{d}{t} = \frac{100.0 m}{12.2 s} = 8.20 m/s$. This average velocity is not the peak velocity but gives us a baseline. Given that the sprinter accelerates for the first half and then maintains a constant velocity, his peak velocity at the 50.0 m mark must be higher than the average to allow for the deceleration in acceleration (even though he maintains this peak speed for the second half). The peak speed, therefore, must be calculated based on the understanding that the time taken to accelerate to peak speed and then maintain it allows for an average speed calculation over the total distance. The correct method involves using kinematic equations to solve for the time to accelerate to 50.0 m, then solving for the velocity at that point, which becomes the constant velocity for the next 50.0 m. However, without explicit acceleration or time to cover the first 50.0 m, we cannot directly calculate it with the given information. The explanation provided here is to clarify the thought process, but the correct answer, based on the need for a detailed calculation that isn't fully provided here, is to recognize that peak speed must be calculated based on the sprinter's acceleration phase and constant velocity phase. Given the options and understanding that the peak speed must be higher than any average speed calculated, option A (12.3 m/s) is selected as the closest to what would be expected for a peak speed in this context, acknowledging that the direct calculation steps are not fully shown here.

A Sprinter Runs 100