How Far Ahead is the Car from the Truck After Passing?

[maplesyrup23]

Homework Statement

A car traveling @ 20 m/s pulls out to pass a truck traveling @ 18m/s. The car accelerates for 2.0m/s^2 for 4s and maintains new velocity.
(c.) If the car was originally 8.0 m behind the truck when it pulled out to pass, how far in front of the truck is the car 10.0 s later?


I did the first two parts, but I got stumpted at the third (above mentioned part c.)

The Attempt at a Solution

I'm 100% sure what I did is wrong. I don't really know where to use the 8.0 m
d = Vi(t) + 1/2 a t^2
= 80m + 100m
= 180 m?

HELP! Thanks in advance. Just trying to go over all physics chapters before the finals. Ntn better to do in the winter hols lolz. Trying to get on the honour roll for the first time ever. Thanks in advance again!

 

[jgens]

Well, start by calculating the total distance traveled by each car.

 

[maplesyrup23]

Using which time?

 

[jgens]

Well, since no other information is given about the truck, assume it travels at constant velocity for 10 seconds. All that's left then is to calculate the distance traveled by the car which can be done in two separate parts: the first when the car is accelerating and the second when it travels at constant velocity for the rest of the time.

 

[maplesyrup23]

okay then,
d(truck)= 18m/s x 10s
= 180m

d(car) = vit + 1/2 at^2

Using 4s, d = 96m
Using 10s, d =300m

Where do I go from here to get my final answer?

 

[jgens]

I agree with your distance traveled for the first four seconds but how did you get 300 for the total distance travelled? The car only accelerates for four seconds not ten. The car travels at constant velocity for six seconds.

 

[maplesyrup23]

Right, right, thanks. So now, how do I find the distance between the car and the truck 10s later? Could you give me the steps? I suspect that I should add the 4s distance and the truck distance... Or is the answer just the 4s distance of the car?

 

[jgens]

Ok, so what is the total distance traveled by the car and what is the total distance traveled by the truck? Use these distances along with the 8 meters to determine how far ahead the car now is.

 

[maplesyrup23]

Alrighty then, thanks much