A sprinter runs 100.0 m. If he travels at constant acceleration of 1.95 m/s² for the first 75.0 m and then at constant velocity for the remaining distance, what was his total elapsed time for the whole race? A) 11.3 s B) 9.8 s C) 10.1 s D) 10.2 s

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Quizplus · Accepted Answer

To solve this problem, we can divide it into two parts: the acceleration phase and the constant velocity phase.1. **Acceleration Phase (First 75.0 m):**Given acceleration $a = 1.95 \, \text{m/s}^2$ and distance $s = 75.0 \, \text{m}$, we can use the equation $s = \frac{1}{2} a t^2$ to find the time $t$ it takes to cover this distance. Rearranging the equation for $t$, we get $t = \sqrt{\frac{2s}{a}}$.Plugging in the given values: $t = \sqrt{\frac{2 \times 75.0}{1.95}} = \sqrt{\frac{150}{1.95}} \approx 8.7 \, \text{s}$.2. **Constant Velocity Phase (Last 25.0 m):**To find the velocity at the end of the acceleration phase, we use $v = at$, where $v$ is the final velocity and $t$ is the time found in the acceleration phase.$v = 1.95 \times 8.7 \approx 16.965 \, \text{m/s}$.This velocity is maintained for the remaining 25.0 m. The time to cover this distance at constant velocity is $t = \frac{s}{v} = \frac{25.0}{16.965} \approx 1.47 \, \text{s}$.3. **Total Time:**Adding the times from both phases gives the total time: $8.7 \, \text{s} + 1.47 \, \text{s} \approx 10.17 \, \text{s}$, which rounds to $10.2 \, \text{s}$, making option D the correct answer.

A Sprinter Runs 100