Final answer:
The final velocity of a sprinter who starts from rest and reaches 10.0 m in 1.9 seconds at constant acceleration is approximately 10.56 m/s. This is calculated by first determining the acceleration using the kinematic equation for displacement, then applying it to find the velocity.
Step-by-step explanation:
Finding the Final Velocity of a Sprinter
To find the final velocity of a runner who starts from rest and sprints 10.0 m in 1.9 seconds with constant acceleration, we can use the kinematic equation:
v = u + at
where:
- v is the final velocity,
- u is the initial velocity (0 m/s, since the runner starts from rest),
- a is the acceleration, and
- t is the time (1.9 seconds).
First, we need to determine the acceleration (a) using the following kinematic equation:
s = ut + 0.5at2
We know that s (displacement) is 10.0 m and u is 0 m/s. By substituting these values into the equation and solving for a, we get:
10.0 m = 0 m/s × 1.9 s + 0.5 × a × (1.9 s)2
After calculation, the acceleration (a) comes out to be approximately 5.56 m/s2. With the acceleration known, we can now determine the final velocity using the first equation:
v = 0 m/s + (5.56 m/s2 × 1.9 s)
Thus, the final velocity of the runner is approximately 10.56 m/s.