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Answer :
The NFL prospect's 40-yard dash time is approximately 5.92 seconds.
How to find dash time?
1. Calculating the time for acceleration:
Using the equation of motion: v = u + at,
where v = final velocity, u = initial velocity, a = acceleration, and t = time.
Given:
Initial velocity (u) = 0 m/s (assuming the prospect starts from rest)
Final velocity (v) = 8.17 m/s
Acceleration (a) = 4.9 m/s²
v = u + at
8.17 = 0 + 4.9t
Solving for t:
t = 8.17 / 4.9
t ≈ 1.67 seconds
2. Calculating the time for the remaining distance:
The remaining distance is 36.6 m - the distance covered during acceleration.
Distance covered during acceleration:
Using the equation of motion: s = ut + (1/2)at²
s = 0 × t + (1/2) × 4.9 × t²
s = (1/2) × 4.9 × t²
Distance covered during acceleration = (1/2) × 4.9 × (1.67)²
Remaining distance = 36.6 m - [(1/2) × 4.9 × (1.67)²]
3. Calculating the time for the remaining distance:
Using the equation of motion: s = vt,
where s is the remaining distance, v is the constant velocity, and t is the time.
s = v × t
[36.6 - (1/2) × 4.9 × (1.67)²] = 8.17 × t
Solving for t:
t = [36.6 - (1/2) × 4.9 × (1.67)²] / 8.17
t ≈ 4.25 seconds
4. Calculating the total dash time:
Total dash time = time for acceleration + time for remaining distance
Total dash time = 1.67 + 4.25
Total dash time ≈ 5.92 seconds
Therefore, the NFL prospect's 40-yard dash time is approximately 5.92 seconds.
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