Answer to Question #80959 in Mechanics | Relativity for Lili

Question

A red car and a green car move towards each other in adjacent lanes and parallel to an x axis. At time t=0, the red car is at x=0, and the green car is at x=220m. If the red car has a constant velocity of 20km/h, the cars pass each other at x=44.5m, and if it has a constant velocity of 40km/h, they pass each other at x=76.6m. What is the initial velocity and constant acceleration of the green car.

Answer 1

The time that cars will pass through with each other:

First variant:

t_1=x_red1/V_red1 =44.5/20*3.6=8.01s
Second variant:
t_2=x_red2/V_red2 =76.6/40*3.6=6.89s
The distances traveled by the green car before meeting with the red:
First variant:
s_green1=x-x_red1=220-44.5=175.5m
Second variant:
s_green2=x-x_red2=220-76.6=143.4m

Equations of motion of the green car:
〖s_green1=V〗_green t_1+(a〖t_1〗^2)/2
〖s_green2=V〗_green t_2+(a〖t_2〗^2)/2
We obtain a system of equations with unknown speed and acceleration of the green car:
〖175.5=8.01V〗_green+32.08a
〖143.4=6.89V〗_green+23.74a
Answer:
Initial velocity and constant acceleration of the green car:
V=14.05 m/s=50.58 km/h
a=1.96 m/s^2