Question

Marissa is standing on the corner waiting for the light to change. The light changes and she starts off running. After 13 seconds of steadily increasing her speed, she is running at 8.0 m/s. How far is she from the light at that moment? *

Answer 1

Marissa, accelerating uniformly from rest, reaches a speed of 8.0 m/s after 13 seconds. Her acceleration is calculated as 0.615 m/s^2, and the distance traveled is found to be 51.975 meters.

Step-by-step explanation:

The student's question is about calculating the distance Marissa has traveled from the light after 13 seconds when she reaches a speed of 8.0 m/s. Assuming Marissa starts from rest and accelerates uniformly, we can use the kinematic equation for uniformly accelerated motion: distance = initial velocity * time + 0.5 * acceleration * time^2, where the initial velocity is zero since she starts from rest. To solve this, we need to find the acceleration, which is the change in velocity over time, so acceleration = final velocity / time. Thus, the acceleration would be 8.0 m/s divided by 13 seconds.

Calculating acceleration: acceleration = 8.0 m/s / 13 s = 0.615 m/s^2. Now we can calculate the distance using the kinematic equation with the initial velocity of 0 m/s, time of 13 seconds, and acceleration of 0.615 m/s^2.

Distance traveled: distance = 0 * 13 + 0.5 * 0.615 m/s^2 * (13 s)^2 = 51.975 meters.

Therefore, Marissa is 51.975 meters away from the light after 13 seconds.