Final answer:
To find the distance traveled by a car accelerating from rest to 15 m/s with an acceleration of 0.45 m/s², we first calculate the time taken to reach this velocity and then use it to compute the distance. The car traveled a total distance of 250 meters during this acceleration.
Step-by-step explanation:
The question asks to calculate the distance traveled by a car that starts from rest and accelerates to a velocity of 15 m/s with an acceleration of 0.45 m/s². This problem can be solved using the kinematic equation which relates initial velocity ({vi}), final velocity ({vf}), acceleration ({a}), and distance ({d}), specifically the equation {d = ((vf + vi) / 2) × t}, where {t} is the time taken to reach the final velocity.
First, we need to determine the time ({t}) by using the equation {vf = vi + (a × t)}, where {vi} is 0 m/s (since the car starts from rest), {vf} is 15 m/s, and {a} is 0.45 m/s². By rearranging the equation, we find {t = vf / a}, which yields {t = 15 m/s / 0.45 m/s² = 33.33 seconds}.
We then calculate the distance using the initial equation: {d = ((0 m/s + 15 m/s) / 2) × 33.33 s = 7.5 m/s × 33.33 s = 250 meters}. Thus, the car traveled a distance of 250 meters while accelerating to a velocity of 15 m/s.