Final answer:
The car travels a distance of 345.6 meters in 12.0 seconds and its final velocity is 28.8 m/s.
Step-by-step explanation:
The car accelerates from rest at a rate of 2.40 m/s² for 12.0 seconds, so we can use the equations of motion to find the unknowns in this problem.
(a) Draw a sketch of the situation:
While entering a freeway, the car starts from rest and accelerates.
(b) List the knowns in this problem:
Initial velocity (vi) = 0 m/s (starting from rest)
Acceleration (a) = 2.40 m/s²
Time (t) = 12.0 s
(c) How far does the car travel in those 12.0 seconds?
To find the distance traveled (d), we can use the kinematic equation:
d = vit + 0.5at²
Plugging in the given values:
d = (0 m/s)(12.0 s) + 0.5(2.40 m/s²)(12.0 s)²
d = 0 + 0.5(2.40 m/s²)(144.0 s²)
d = 0 + 345.6 m
d = 345.6 m
Therefore, the car travels a distance of 345.6 meters in those 12.0 seconds.
(d) What is the car's final velocity?
To find the final velocity (vf), we can use another kinematic equation:
vf = vi + at
Plugging in the given values:
vf = 0 m/s + (2.40 m/s²)(12.0 s)
vf = 0 m/s + 28.8 m/s
vf = 28.8 m/s
Therefore, the car's final velocity is 28.8 m/s.