The car, initially traveling at 5.0 m/s and accelerating uniformly at 2.0 m/s² for 10 seconds, travels a total distance of 150 meters, based on the kinematic equation for distance with constant acceleration. However, there is likely an error in the question as this option is not provided.
Uniform Acceleration and Distance Traveled
To find the total distance traveled by the car during a 10-second interval with uniform acceleration, we can use the kinematic equation for distance with constant acceleration, which is:
d = vi*t + 1/2*a*t²
Where d is the distance, vi is the initial velocity, a is the acceleration, and t is the time.
Given that the initial velocity (vi) is 5.0 m/s, acceleration (a) is 2.0 m/s², and time (t) is 10 seconds, we can calculate the distance:
d = 5.0 m/s * 10 s + 1/2 * 2.0 m/s² * (10 s)²
d = 50 m + 1/2 * 2.0 m/s² * 100 s²
d = 50 m + 100 m
d = 150 m
Thus, the car travels a total distance of 150 meters during the 10-second interval.
However, since the option of 150 meters is not provided in the multiple-choice answers, it appears there may have been an error in the question or a misunderstanding. It's essential always to verify the information and question details before solving.