Question

A sprinter runs the curve of this 200 m in 10.28 s. Assume he ran in a lane which makes a semicircle (r = 33.7 m) for the first part of the race. At 3.74 s into the race his speed is 4.5 m/s. At 7.5 s into the race his speed is 8.4 m/s. His speed after the curve was 12.1 m/s.

What was the sprinter's radial acceleration at 3.74 s? to 3 decimal places

Answer 1

The sprinter's radial acceleration at 3.74 s is approximately 2.03 m/s².

Step-by-step explanation:

To calculate the sprinter's radial acceleration at 3.74 s, we first need to find the speed at that time. From the given information, we know that his speed at 3.74 s is 4.5 m/s and his final speed after the curve is 12.1 m/s. The change in speed during that time is 12.1 m/s - 4.5 m/s = 7.6 m/s.

Next, we can use the formula for radial acceleration:

radial acceleration = change in speed / time

Substituting the values, we get:

radial acceleration = 7.6 m/s / 3.74 s = 2.03 m/s²

Therefore, the sprinter's radial acceleration at 3.74 s is approximately 2.03 m/s².