Final answer:
The acceleration of the car is 2 m/s², and the distance traveled during this time is 114 meters.
Step-by-step explanation:
To calculate the car's acceleration, we can use the formula:
a = Δv / t
where Δv is the change in velocity, and t is the time. The change in velocity (Δv) is the final velocity (v_f) minus the initial velocity (v_i), which is 25 m/s - 13 m/s = 12 m/s. The time (t) given is 6.0 seconds.
Plugging the values in:
a = 12 m/s / 6.0 s = 2 m/s²
So, the acceration of the car is 2 m/s².
To calculate the distance traveled, we can use the formula derived from the equations of motion:
d = v_i • t + (1/2) • a • t²
Inserting the known values (v_i = 13 m/s, a = 2 m/s², t = 6.0 s):
d = (13 m/s • 6.0 s) + (1/2 • 2 m/s² • (6.0 s)²) = 78 m + 36 m = 114 m
The car traveled a distance of 114 meters.