A truck is stopped at a stoplight. When the light turns green, it accelerates at 2.7 m/s2. At the same instant, a car passes the truck going 18 m/s. Where and when does the truck catch up with the car?

Don't they go the same distance in the same time?

distance car= 18*time
distancetruck=1/2 2.7 t^2
set them equal, solve for time.

need answer fast- running out of time

bob, i appreciate your help with questions like these but don't be so harsh on Dylan. My teacher didn't explain this very well and so I think we're both just struggling with this subject.

To determine where and when the truck catches up with the car, we need to find the time it takes for the truck to catch up and the distance traveled by both vehicles during that time.

Let's assume that at time t = 0, both the truck and the car are at the same point.

First, we need to find the time it takes for the truck to catch up with the car. To do that, we can use the equation of motion:

s = ut + (1/2)at^2

Where:
s is the distance traveled
u is the initial velocity
a is the acceleration
t is the time

For the car:
The initial velocity (u) is 18 m/s and the acceleration (a) is 0 m/s^2 (since the car is not accelerating).
For the truck:
The initial velocity (u) is 0 m/s (since it is stopped) and the acceleration (a) is 2.7 m/s^2.

Since the truck catches up with the car, their final positions will be the same. So, we can equate the distances traveled by both vehicles:

18t = (1/2)(2.7)t^2

Simplifying the equation, we get:

18t = 1.35t^2

Rearranging the equation, we have:

1.35t^2 - 18t = 0

Factoring out t, we get:

t(1.35t - 18) = 0

From this equation, we can determine two possible values for t: t = 0 and t = 13.33 seconds.

Since t = 0 represents the initial time when both vehicles are at the same point, we can discard it. Therefore, t = 13.33 seconds.

Now that we know the time it takes for the truck to catch up, we can find the distance traveled by both vehicles during that time.

For the car:
Distance traveled = velocity × time = 18 m/s × 13.33 s = 239.94 meters

For the truck:
Distance traveled = initial velocity × time + (1/2) × acceleration × time^2
= 0 m/s × 13.33 s + (1/2) × 2.7 m/s^2 × (13.33 s)^2
= 120.02 meters

Therefore, the truck catches up with the car after traveling approximately 120.02 meters, and this happens 13.33 seconds after the start.

Note: Since we assumed both vehicles started from the same point, it is important to consider the scenario might be different based on the actual starting positions of the vehicles.

I am not going to do it for you. Why did you wait so late to start it? This is a rather elementary question.

I worked it out, goodness. you set the two distances equal, and solve for time. it takes two lines of algebra, about 20 seconds. Instead of that, the request was for the answer. Sorry.