Question

While entering a freeway, a car accelerates from rest at a rate of 2.40 m/s² for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? (d) What is the car’s final velocity?

a) (a) Not provided, (b) Not provided, (c) 17.28 m, (d) 28.8 m/s
b) (a) Not provided, (b) Not provided, (c) 34.56 m, (d) 57.6 m/s
c) (a) Not provided, (b) Not provided, (c) 46.08 m, (d) 76.8 m/s
d) (a) Not provided, (b) Not provided, (c) 51.84 m, (d) 86.4 m/s

Answer 1

The car travels a distance of 172.8 m in 12.0 s and has a final velocity of 28.8 m/s.

Step-by-step explanation:

(a) Draw a sketch:

(b) List the knowns in this problem: The acceleration (a) is 2.40 m/s², the time (t) is 12.0 s, the initial velocity (vo) is 0 m/s, and the initial position (xo) is 0 m.

(c) To find how far the car travels in those 12.0 s, we can use the equation x = xo + vot + 1/2at². Plugging in the values, we get x = 0 + 0 + (1/2)(2.40 m/s²)(12.0 s)² = 172.8 m.

(d) The final velocity (v) can be found using the equation v = vo + at. Plugging in the values, we get v = 0 + (2.40 m/s²)(12.0 s) = 28.8 m/s.