Question

A sprinter is running at the end of a race and begins to tire. Her velocity is 8.55 m/s and has negative acceleration at -0.1 m/s^2 for the last 80 meters. What is her velocity when she ends the race?

a) 7.75 m/s
b) 9.35 m/s
c) 8.05 m/s
d) 6.45 m/s

Answer 1

To find the sprinter's velocity when she ends the race, we can use the equation vf = vi + at. Substituting the given values, we find that the final velocity is approximately 7.75 m/s. Therefore, the correct option is a) 7.75 m/s.

Step-by-step explanation:

To find the final velocity of the sprinter when she ends the race, we can use the equation:

vf = vi + at

Where:
vf = final velocity
vi = initial velocity (8.55 m/s)
a = acceleration (-0.1 m/s²)
t = time

Since we are given the acceleration and the final distance (80 meters), we can find the time using the equation:

d = vi * t + 0.5 * a * t²

Substituting the known values, we have:

80 = 8.55 * t + 0.5 * (-0.1) * t²

Simplifying and solving the quadratic equation, we find that t ≈ 11.21 seconds.

Now, we can substitute this value of t into the first equation to find the final velocity:

vf = 8.55 + (-0.1) * 11.21

Calculating this, we get vf ≈ 7.75 m/s. Therefore, the sprinter's velocity when she ends the race is approximately 7.75 m/s. So the correct option is a) 7.75 m/s.