How fast will the car be traveling at that instant?

[machinegun]

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.3 m/s2. At the same instant a truck, traveling with a constant speed of 9.6 m/s, overtakes and passes the automobile.
(a) How far beyond the traffic signal will the automobile overtake the truck?

(b) How fast will the car be traveling at that instant?

Not exactly sure how to set the problem up. Like exactly how does the truck's speed help find the answer? I know I need to find the time it took to figure out the rest. I'm just missing something in the the question that will help set up the problem.

 

[Farsight]

You're looking for two equal distances where the time is also the same:

s_car = .5 * at² = s_truck = vt

 

[kyle8921]

I would approach this problem using the principles of kinematics, specifically the equations of motion for objects with constant acceleration. The information given in the problem can be used to calculate the time it takes for the automobile to overtake the truck, and from there we can find the distance and the velocity of the car at that instant.

(a) To find the time it takes for the car to overtake the truck, we can use the equation d = v0t + 1/2at^2, where d is the distance traveled, v0 is the initial velocity (in this case, 9.6 m/s for the truck), a is the acceleration (2.3 m/s^2 for the car), and t is the time. Since the car starts from rest, v0 is equal to 0, and the equation becomes d = 1/2at^2. Rearranging for t, we get t = √(2d/a). We know that the car and the truck will have traveled the same distance when the car overtakes the truck, so we can set the distance traveled by the car (d) equal to the distance traveled by the truck (9.6t). This gives us the equation 9.6t = 1/2at^2. Solving for t, we get t = 19.2/a = 19.2/2.3 = 8.35 seconds. This is the time it takes for the car to overtake the truck.

(b) Now that we know the time it takes for the car to overtake the truck, we can use the equation v = v0 + at to find the velocity of the car at that instant. Since we know the initial velocity of the car is 0, the equation becomes v = at. Plugging in the acceleration (2.3 m/s^2) and the time (8.35 seconds), we get v = 2.3*8.35 = 19.2 m/s. This is the velocity of the car at the instant it overtakes the truck.

In conclusion, the car will overtake the truck after traveling a distance of 9.6 m/s * 8.35 s = 80.16 meters beyond the traffic signal. At that instant, the car will be traveling at a velocity of 19.2 m/s. The truck's speed was not directly