At the instant a traffic light turns green, an automobile that has been waiting at an intersection starts moving forward with a constant acceleration of 2.00m/s(squared). At the same time a truck traveling with a constant speed of 18m/s, overtakes and passes the automobile.

1.How for beyond the starting point does the automobile overtakes the truck?
2.How fast is the automobile traveling when it overtakes the truck?

Someone please help me with this question!!!

They both go the same distance, in the same time.

distancetruck=18(t)
distance car=1/2 *2*t^2
set them equal, solve for time t.
How far? 18t
how fast auto? 2*t

How woukd you graph the position of each vehicle as a function of time.(0 being the traffic light)

To solve this problem, we need to calculate the distance and velocity of the automobile at the point where it overtakes the truck.

1. Calculating the distance:
Let's assume that the automobile overtakes the truck after time t.

The automobile's initial velocity, u = 0 m/s (as it starts from rest)
The automobile's acceleration, a = 2.00 m/s²

Using the kinematic equation: s = ut + 0.5at², where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.

For the automobile:
s = 0 * t + 0.5 * 2.00 * t²
s = 0 + 1.00t²
s = 1.00t²

For the truck:
The truck's velocity, v = 18 m/s
The truck travels the same amount of time as the automobile, so the distance traveled by the truck, S = v * t.

Since the automobile overtakes the truck, the distance traveled by the automobile must be greater than the distance traveled by the truck. Therefore, we can set the two distances equal to each other and solve for t:

1.00t² = 18t
t(1.00t - 18) = 0
t = 0 (ignore) or t = 18/1.00
t = 18 seconds

Substituting this value of t back into the equation for distance traveled by the automobile:

s = 1.00 * (18)²
s = 1.00 * 324
s = 324 meters

Therefore, the automobile overtakes the truck at a point 324 meters beyond the starting point.

2. Calculating the velocity:
Now, we can calculate the velocity of the automobile when it overtakes the truck using the equation v = u + at.

For the automobile:
u = 0 m/s (initial velocity)
a = 2.00 m/s² (acceleration)
t = 18 seconds (time taken to overtake the truck)

v = 0 + 2.00 * 18
v = 0 + 36
v = 36 m/s

Therefore, the automobile is traveling at a velocity of 36 m/s when it overtakes the truck.

To solve this problem, we can use the equations of motion to find the answers to the questions.

1. To find how far beyond the starting point the automobile overtakes the truck, we need to determine the time it takes for the automobile to catch up with the truck.

Let's assume that the automobile overtakes the truck at time t. During this time, the truck travels a distance equal to the length of the truck, L, which we need to find.

For the truck:
Distance = Speed × Time
L = (18 m/s) × t

For the automobile:
Distance = Initial Velocity × Time + 0.5 × Acceleration × Time^2
Here, the initial velocity of the automobile is zero, as it starts from rest at the green light.
Distance = 0 × t + 0.5 × (2.00 m/s^2) × t^2

Since the automobile overtakes the truck when they cover the same distance, we can set the two equations equal to each other:
L = (18 m/s) × t = 0.5 × (2.00 m/s^2) × t^2

Now, we have an equation with one unknown, t, which we can solve to find the time. Once we find the time, we can substitute it in the equation for the distance traveled by the automobile to find the answer to the first question.

2. To find the speed of the automobile when it overtakes the truck, we can use the equation of motion:

Final Velocity = Initial Velocity + Acceleration × Time

Here, the initial velocity of the automobile is zero, and we already know the acceleration and the time it takes to overtake the truck, which we find in step 1. We can substitute these values into the equation to find the final velocity of the automobile when it overtakes the truck, which will be the answer to the second question.

By following these steps, you can find the answers to both questions.