Question

Guys I have a physics 1 question. It has a graph, but I dont think it needs the graph. It states:

A car starts at x=4 and has a velocity given by the following graph. At what time does he collide with another car that starts at x=20 with velocity v=-2m/s

to explain the graph they Y axis has even spacing 2, 4, 6 and is labeled V (m/s) and the X axis is evenly spaced by 2 as well and is labeled as t(s)

can someone help solve this? I know that i have to get rid of that -2 somehow and get time by itself.

Answer 1

I've attached the graph

Answer 2

from the graph, we can write:
\[\Large {v_A} = 3.6t\]
for the first car
so, integrating once, we get:
\[\Large {x_A}\left( t \right) = 1.8{t^2} + 4\]
whereas for the second car, we can write:
\[\Large {x_B}\left( t \right) = 20 - 2t\]
collision will happens, at time \(\tau\) such that:
\[\Large {x_A}\left( \tau \right) = {x_B}\left( \tau \right)\]
or:
\[\Large 1.8{\tau ^2} + 4 = 20 - 2\tau \]