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 9.4 m/s, overtakes and passes the automobile.

(a) How far beyond the traffic signal will the automobile overtake the truck?
m
(b) How fast will the car be traveling at that instant?
m/s

at some time t, the same time for both cars, they have went the same distance d.

You have two equations

Truck: d=vi*t
Car: d=1/2 a t^2

set the equal, solve for t, thensolve for d.

To solve this problem, we can use the kinematic equations of motion. We'll need to find the time it takes for the car to overtake the truck and then calculate the distance and speed at that instant.

(a) First, let's find the time it takes for the car to overtake the truck. We can use the equation:

distance = initial velocity * time + (1/2) * acceleration * time^2

Since the initial velocity of the car is 0 (assuming it starts from rest), the equation becomes:

distance = (1/2) * acceleration * time^2

We need to find the time when the distance covered by the car is equal to the distance covered by the truck. The distance covered by the truck can be calculated as:

distance_truck = velocity_truck * time

Setting the two distances equal to each other:

(1/2) * acceleration * time^2 = velocity_truck * time

Simplifying and rearranging the equation:

(1/2) * acceleration * time = velocity_truck

Substituting the given values:

(1/2) * 2.3 m/s^2 * time = 9.4 m/s

Solving for time:

time = (2 * 9.4 m/s) / (2.3 m/s^2) ā‰ˆ 8.17 s

Now that we have the time it takes for the car to overtake the truck, we can calculate the distance covered by the car:

distance_car = (1/2) * acceleration * time^2
distance_car = (1/2) * 2.3 m/s^2 * (8.17 s)^2 ā‰ˆ 70.40 m

Therefore, the car will overtake the truck approximately 70.40 m beyond the traffic signal.

(b) To find the speed of the car at that instant, we can use the kinematic equation:

final speed = initial speed + acceleration * time

Since the initial speed of the car is 0, the equation becomes:

final speed = acceleration * time

Substituting the given values:

final speed = 2.3 m/s^2 * 8.17 s ā‰ˆ 18.81 m/s

Therefore, the car will be traveling at approximately 18.81 m/s when it overtakes the truck.