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?

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To answer these questions, we need to analyze the motion of the automobile and the truck.

1. How far beyond the starting point does the automobile overtake the truck?

We can start by finding the time it takes for the automobile to catch up to the truck. Since the truck is moving at a constant speed, the time it takes for the automobile to catch up is the same as the time it takes for the automobile to cover the distance traveled by the truck.

Let's denote the distance covered by the automobile as Sauto and the distance covered by the truck as Struck. Since the automobile starts from rest, we can use the formula of motion Sauto = u*t + (0.5)*a*t^2, where u is the initial velocity, a is the acceleration, and t is the time.

For the automobile:
Initial velocity, uauto = 0 m/s
Acceleration, aauto = 2.00 m/s^2

For the truck:
Speed of truck, vtruck = 18 m/s

To find the time it takes for the automobile to catch up to the truck, we can set the distances equal to each other: Sauto = Struck.

Using the formula for the distance covered by the automobile, Sauto = (0.5)*aauto*tauto^2, and the distance covered by the truck, Struck = vtruck*ttruck, we can set up the equation:

(0.5)*aauto*tauto^2 = vtruck*ttruck

Simplifying, we have:
0.5*2.00*t^2 = 18t

Rearranging the equation:
t^2 - 18t = 0

Factoring out t:
t(t - 18) = 0

Therefore, t = 0 or t = 18.

Since we are interested in the time it takes for the automobile to catch up to the truck, we discard the t = 0 solution. So, t = 18 seconds.

Now, we can calculate the distance covered by the automobile. Plugging the value of t into the equation for Sauto, we have:
Sauto = (0.5)*aauto*t^2
Sauto = (0.5)*(2.00)*(18)^2

Simplifying, we find:
Sauto = 324 meters

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

2. How fast is the automobile traveling when it overtakes the truck?

To find the speed of the automobile at the moment it overtakes the truck, we can use the formula of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Since the truck is traveling at a constant speed, the final velocity of the truck is also the initial velocity of the automobile when it overtakes the truck. Therefore, the final velocity of the truck is vtruck = 18 m/s.

Using the formula of motion, we have:
vauto = uauto + aauto*t

Plugging in the values, we have:
vauto = 0 + (2.00)*(18)

Simplifying, we find:
vauto = 36 m/s

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