A sprinter accelerates at the start of the race at 8.5 m/s^2. After 1.3 seconds the sprinter runs the rest of the 100m race at a constant velocity. What was the sprinter's time at the finish line?
To find the sprinter's time at the finish line, we need to determine the time it takes for the sprinter to accelerate and the time it takes for the sprinter to run the rest of the race at a constant velocity.
First, let's find the time it takes for the sprinter to accelerate. The sprinter accelerates at a rate of 8.5 m/s^2 for 1.3 seconds. We can use the formula for acceleration to find the final velocity (v) during the acceleration period:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since the sprinter starts from rest (u = 0), the equation simplifies to:
v = at
Plugging in the values:
v = (8.5 m/s^2)(1.3 s)
v ≈ 11.05 m/s
Now, we need to find the time it takes for the sprinter to run the remaining 100 m at a constant velocity. Since the sprinter runs at a constant velocity, we know that the distance (d) is equal to the product of the velocity (v) and time (t):
d = vt
We know the distance and velocity, so we can rearrange the equation to solve for time:
t = d / v
Plugging in the values:
t = (100 m) / (11.05 m/s)
t ≈ 9.04 s
Therefore, the sprinter's time at the finish line is approximately 9.04 seconds.