At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.1 m/s^2. At the same instant a truck, traveling with a constant speed of 9.2 m/s, overtakes and passes the automobile ?
1 Answer
Time needed:
Speed of car:
Explanation:
FULL QUESTION
At the instant the traffic light turns green, an automobile starts with a constant acceleration a of
(a) How far beyond the traffic signal will the automobile overtake the truck?
(b) How fast will the automobile be traveling at that instant?
This one is pretty straightforward. You know that at
At the same time, a truck moving at a speed of
The idea here is that the distance they travel until the car overtakes the truck is the same for both the car, and the truck.
The same can be said for the time that passes until the two meet again.
So, if the car takes a time
#d = v * t -># for the truck
and
#d = underbrace(v_0)_(color(blue)(=0)) * t + 1/2 * a * t^2 -># for the car
This will get you
#v * color(red)(cancel(color(black)(t))) = 1/2 * a * t^color(red)(cancel(color(black)(2))) implies t = (2 * v)/a#
#t = (2 * 9.2color(red)(cancel(color(black)("m")))/color(red)(cancel(color(black)("s"))))/(2.1color(red)(cancel(color(black)("m")))/"s"^color(red)(cancel(color(black)(2)))) = "8.76 s"#
This means that the distance is
#d = v * t = 9.2"m"/color(red)(cancel(color(black)("s"))) * 8.76color(red)(cancel(color(black)("s"))) = color(green)("80.6 m")#
The speed of the car is
#v_"car" = a * t = 2.1"m"/"s"^color(red)(cancel(color(black)(2))) * 8.76color(red)(cancel(color(black)("s"))) = color(green)("18.4 m/s")#
