Final answer:
To calculate the distance traveled by a car that accelerates from rest to 25 m/s, the kinematic equation vf^2 = vi^2 + 2ad is used, resulting in a distance of approximately 78.125 m.
Step-by-step explanation:
The question involves calculating the distance traveled by a car that accelerates from rest to a certain velocity. To find the distance (df) the car has traveled once its velocity reaches 25 m/s (vf = 25 m/s), we use one of the kinematic equations of motion, which relates initial velocity (vi), final velocity (vf), acceleration (a), and distance traveled (df).
The appropriate formula to use in this case is vf2 = vi2 + 2ad, where vi = 0 m/s (since the car starts at rest), vf = 25 m/s (the final velocity), a = 4 m/s2 (the acceleration), and d is what we need to find.
Plugging in the known values, we get:
252 = 02 + 2 × 4 × d
625 = 8d
d = 625 / 8
d = 78.125 m
So the distance traveled by the car is approximately 78.125 meters. Looking at the given options, none of them exactly matches the calculated distance, but the closest answer to the actual distance would be (b) 100 m as the most reasonable approximation.