Car in northbound lane with acceleration going towards car in southbound lane 300m away going 25 m/s. When will they pass each other?

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/s2m/s2. At this moment there is also a car in the southbound lane that is 300 m away and traveling at a constant 25 m/sm/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?

How far from the red light are they when they pass each other?

Answer 1

You can derive position/time equations for each, but you must make sure the origin and time are in the same frame:

The accelerating car (starts at x=0 at t=0): x - x₀ = v₀t + (1/2)at² or x = (1/2)at²

The constant velocity car: x-x₀ = vt or x = x₀ + vt

Plugging in the numbers (all units are MKS, so they mesh)

x_NB = (1/2)(2)t² = t² and x_SB = 300 - 25t (Note that v is negative, x₀ and a are positive, choosing N as +)

We want to know when the NB and SB cars are at the same position for the same time (equate the positions and solve for t)

t² = 300 - 25t (You can now use quadratic formula to solve for t and sub into equations for x)

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