A 1000-kg automobile enters a freeway on-ramp at 20 m/s and accelerates uniformly up to 40 m/s in a time of 10 seconds. How far does the automobile travel during that time?
A)100 m
B)200 m
C)300 m
D)400 m
E)none of the above

Question

Quizplus · Accepted Answer

Using the formula for distance traveled during uniform acceleration:
d = 0.5(a)(t^2) + v_i(t)

Where d is the distance traveled, a is the acceleration, t is the time, and v_i is the initial velocity.

Since the automobile is accelerating uniformly from 20 m/s to 40 m/s in 10 seconds:
a = (40-20)/10 = 2 m/s^2
v_i = 20 m/s
t = 10 s

Plugging in these values to the formula, we get:
d = 0.5(2)(10^2) + 20(10)
d = 100 + 200
d = 300 m

Therefore, the automobile travels a distance of 300 meters during that time.

A 1000-Kg Automobile Enters a Freeway On-Ramp at 20 M/s