While passing a slower car on the highway, you accelerate uniformly from 18.5 m/s to 29.3 m/s in a time of 12.0 s. How far do you travel during this time?
(average velocity)*(time)
= 23.9 m/s*12 s
= 286.8 m
To determine the distance traveled during this time, we can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
In this case, the initial velocity is given as 18.5 m/s, and the final velocity is 29.3 m/s. The time is given as 12.0 s. Since the acceleration is uniform, we can calculate it using the equation:
acceleration = (final velocity - initial velocity) / time
Let's calculate the acceleration first:
acceleration = (29.3 m/s - 18.5 m/s) / 12.0 s
acceleration = 10.8 m/s / 12.0 s
acceleration = 0.9 m/s^2
Now, we can substitute the values into the distance equation:
distance = 18.5 m/s * 12.0 s + 0.5 * 0.9 m/s^2 * (12.0 s)^2
distance = 222 m + 0.5 * 0.9 m/s^2 * 144 s^2
distance = 222 m + 0.5 * 0.9 m/s^2 * 20,736 s^2
distance = 222 m + 9,331.2 m
distance = 9,553.2 m
Therefore, you would travel a distance of approximately 9,553.2 meters during this time.