Solving for Runner's Speed at End of Race | Physics Homework Help

[jwang023]

Homework Statement

I figured out the speed of the runner at t=2.0 seconds, but I am stuck on finding v of the runner at the end of the race.

Q: At the starting gun, a runner accelerates at 1.7 m/s^2 for 4.8 seconds. The runner's acceleration is zero for the rest of the race. what is the speed of the runner at the end of the race?

Homework Equations

The Attempt at a Solution

 

[jwang023]

never mind! Figured it out!

 

[kerimek]

First, we can use the equation v = u + at to calculate the final velocity (v) of the runner at the end of the 4.8 seconds of acceleration. We know that the initial velocity (u) is 0 m/s, as the runner starts from rest. We also know that the acceleration (a) is 1.7 m/s^2 and the time (t) is 4.8 seconds. Plugging these values into the equation, we get: v = 0 + (1.7 m/s^2)(4.8 s) = 8.16 m/s.

Next, we can use the equation v^2 = u^2 + 2as to calculate the final velocity (v) of the runner at the end of the race, where the acceleration (a) is 0 m/s^2 and the displacement (s) is the distance covered during the 4.8 seconds of acceleration. We can calculate the distance using the equation s = ut + 0.5at^2, where u is the initial velocity (0 m/s) and t is the time (4.8 seconds). Plugging these values into the equation, we get: s = (0 m/s)(4.8 s) + 0.5(1.7 m/s^2)(4.8 s)^2 = 36.864 m. Now, we can plug this value into the first equation to solve for v: v = √(0^2 + 2(0 m/s^2)(36.864 m)) = 0 m/s.

Therefore, the speed of the runner at the end of the race is 0 m/s, as the runner will have stopped moving after the initial 4.8 seconds of acceleration.