Finding distance with Kinematics

[Becca93]

Homework Statement

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 88.0 km/hr approaches a car stopped at the red light. When the truck is 125.3 meters from the car the light turns green and the car immediately begins to accelerate at 2.50 m/s2 to a final speed of 102.0 km/hr.

How close does the truck come to the car assuming the truck does not slow down?

How far from the stop light has the car traveled when the truck reaches its closest distance?

The Attempt at a Solution

I've tried solving this by finding how long it takes for the car to reach the same velocity as the truck, seeing how far it went, and getting the distance between them. But the answer isn't correct and I have no idea how else to proceed.

 

[ex81]

what equations have you tried?

here are a couple kinematic equations:

https://www.physicsforums.com/showthread.php?t=110015

p.S. the final speed of the car isn't really relevant as that is beyond the closest point the semi will get to the car. The closest they will get is when the car makes it to the 88km/h. So which equation would you use in terms of acceleration, final velocity, and time for the car?

 

[NewtonianAlch]

First time I've heard of trying to save fuel by going at a constant speed, fuel consumption is more dependent on the rpm rather than the speed by itself.

 

[ex81]

it is pretty common technique. Granted, it does assume a level surface in which case said truck would be in the highest gear, and thus least amount of fuel going to the engine.

 

[Becca93]

what equations have you tried?

here are a couple kinematic equations:

https://www.physicsforums.com/showthread.php?t=110015

p.S. the final speed of the car isn't really relevant as that is beyond the closest point the semi will get to the car. The closest they will get is when the car makes it to the 88km/h. So which equation would you use in terms of acceleration, final velocity, and time for the car?

I used v2=v20+2aΔx to get distance covered by the car, and I did get the correct answer which was 119.07m when I used the van's velocity as v2 like you said. I got time using d=v1t+(1/2)at2 (cancelling v1 because because the initial velocity of the car is zero), which gave me t= 9.76 seconds.

My big issue from there, however, is determining the closest distance the van gets to the car. I tried adding the 125.3m to the 119.07, and then subtracting the distance the van traveled over in that time. But that answer isn't being accepted as correct and I am honestly lost as to how to proceed.

 

[ex81]

That 125.3, and 119.7m combined is the total distance from where the van was until the car got up to speed. Not how far the van moved during those 9.76 seconds

How far did the van travel during the time it took the car to accelerate up to 88km/h? Your are going to convert that into m/s, and multiply that by the 9.76 seconds.

distance = v*t

so total distance covered by the truck is 238.57m

245 is my total for the distance at start from the truck, and the car's start in addition to the car's acceleration up to 88km/h

P.S. always check you units. It is where most of us miss stuff

 

[Becca93]

How far did the van travel during the time it took the car to accelerate up to 88km/h? Your are going to convert that into m/s, and multiply that by the 9.76 seconds.

I get 238.58 m. But when I add 119.072 and 125.3 (resulting in 244.372), and subtract 238.58, the answer is incorrect. I don't understand what I'm doing wrong.

Edit: I caught my issue. Not carrying enough significant digits threw my answer by a few points and it was causing the answer to be rejected. Thanks for everything, though!