Question

A car in the northbound lane is sitting at a red light. At

the moment the light turns green, the car accelerates
from rest at 2.0 m/s2. At this moment there is also a
car in the southbound lane that is 240 m away and
traveling at a constant 25 m/s. The northbound car
maintains its acceleration until the two cars pass each
other.
How long after the light turns green do the cars pass each other?

Answer 1

7.41 sec

Step-by-step explanation:

let distance southbound car travels = 240 - x

let distance northbound car travels = x

Use these equations:

x = vt

x = Vit + 1/2at² (Vi = 0)

1) 240 - x = (25 m/s)t

2) x = 0 + 1/2(2.0 m/s²)t²

x = t² substitute this into equation 2)

240 - t² = (25 m/s)t

rearrange into a quadratic equation and solve for t using the quadratic formula:

-t² = 25t - 240

t² + 25t -240 = 0

t = 7.406, -32.406

disregard the negative root

final answer: t ≈ 7.41 s