Jennifer is running the 100.0 m dash at track. She accelerates at a rate of 0.88 m/s2 for thefirst 45 m and then maintains this speed for the remainder of the race. How long will it takeher to finish the race? (Answer: t= 10.1 s + 6.2 s=16.3 s)
Question
Jennifer is running the 100.0 m dash at track. She accelerates at a rate of 0.88 m/s2 for thefirst 45 m and then maintains this speed for the remainder of the race. How long will it takeher to finish the race? (Answer: t= 10.1 s + 6.2 s=16.3 s)
Solution
To solve this problem, we need to break it down into two parts: the time it takes for Jennifer to accelerate to her top speed, and the time it takes for her to run the remaining distance at that speed.
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First, we need to find out how long it takes for Jennifer to accelerate to her top speed. We can use the formula for time (t) in uniformly accelerated motion, which is t = √(2d/a), where d is the distance (45 m) and a is the acceleration (0.88 m/s²). Plugging in these values, we get t = √(2*45/0.88) = 10.1 seconds.
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Next, we need to find out Jennifer's top speed. We can use the formula for final velocity (v) in uniformly accelerated motion, which is v = at, where a is the acceleration (0.88 m/s²) and t is the time we just calculated (10.1 s). Plugging in these values, we get v = 0.8810.1 = 8.9 m/s.
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Now we need to find out how long it takes for Jennifer to run the remaining distance at her top speed. The remaining distance is 100 m - 45 m = 55 m. The time it takes to cover this distance at a constant speed is given by the formula t = d/v, where d is the distance (55 m) and v is the velocity (8.9 m/s). Plugging in these values, we get t = 55/8.9 = 6.2 seconds.
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Finally, we add the two times together to get the total time it takes for Jennifer to finish the race. This is 10.1 s + 6.2 s = 16.3 s.
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