At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 2.85m/s^2. At the same instant a truck, traveling with a constant speed of 19.0m/s, overtakes and passes the car.

A) How far beyond its starting point does the car overtake the truck?

B) How fast is the car traveling when it overtakes the truck?

a) they both travel the same distance in the same time.

distancecar=distancetruck
1/2 * 2.85*t^2=19*t
solve for t, then solve for either distance.

b) vf=2.85*t

To answer these questions, we need to analyze the motion of the car and the truck. Let's break it down step by step.

Step 1: Find the time it takes for the car to catch up to the truck.
To do this, we first need to determine the time it takes for the car to accelerate to the same speed as the truck. We can use the equation:
v = u + at,
where
v is the final velocity (speed),
u is the initial velocity (speed),
a is the acceleration,
and t is the time.

Let's denote the initial velocity of the car as u_car and the initial velocity of the truck as u_truck.

Given:
Acceleration of the car, a_car = 2.85 m/s^2,
Initial velocity of the car, u_car = 0 m/s (as it starts from rest),
Speed of the truck, u_truck = 19.0 m/s.

Using the equation v = u + at for the car,
19.0 m/s = 0 m/s + 2.85 m/s^2 * t.
Solving for t, we get:
t = 19.0 m/s / 2.85 m/s^2.

Step 2: Calculate the distance traveled by the car.
To find the distance the car travels while accelerating, we use the equation:
s = u_car * t + (1/2) * a_car * t^2,
where
s is the distance traveled,
u_car is the initial velocity of the car,
t is the time,
and a_car is the acceleration of the car.

Substituting the known values,
s = 0 m/s * t + (1/2) * 2.85 m/s^2 * (t)^2.

Step 3: Calculate the distance the truck has covered during this time.
Since the truck is traveling with a constant speed, we can use the equation:
s_truck = u_truck * t.

Step 4: Determine the distance the car overtook the truck.
The distance the car overtook the truck is given by:
Distance = Total distance covered by the car - Distance covered by the truck.

Using the calculated values, we can substitute and find the answer to part A.

Step 5: Determine the speed of the car when it overtakes the truck.
To find the speed of the car when it overtakes the truck, we can use the equation:
v = u_car + a_car * t.

Substituting the known values, we can find the answer to part B.

Now, let's calculate the answers to the two questions using the given values.