Solved: Acceleration Problem for Truck and Car

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Homework Help Overview

The problem involves a truck and a car, focusing on the dynamics of acceleration and relative motion. The truck maintains a constant speed while the car accelerates from rest at a specified rate. The goal is to determine how close the truck comes to the car as they move.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the time it takes for the truck to reach the car and questions how to determine the point at which their velocities are equal. Other participants inquire about the time required for the car to reach the truck's speed and the distances traveled by both vehicles during that time.

Discussion Status

The discussion includes various calculations and attempts to understand the relationship between the distances traveled by the truck and car. Some participants provide numerical estimates, but there is no explicit consensus on the final outcome or resolution of the problem.

Contextual Notes

Participants are working under the constraints of the problem as presented, including the truck's constant speed and the car's acceleration. The original poster expresses uncertainty about the next steps after initial calculations.

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[SOLVED] Acceleration problem

To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 85.0 km/hr approaches a car stopped at the red light. When the truck is 84.6 meters from the car the light turns green and the car immediately begins to accelerate at 3.60 m/s2 to a final speed of 88.0 km/hr. How close does the truck come to the car assuming the truck does not slow down?

First off I converted 85km/hr to m/s ... Truck is traveling ~23.6m/s

Then I calculated that it would take the Truck ~3.58 s to reach the stopped car (84.5/23.6=3.58)

Now the truck is closest to the car when their velocities are equal to each other.. but I don't know where to go from there.

Any help would be appreciated.
 
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How long will it take for the car to accelerate to the velocity of the truck?
 
~6.55 s
 
So how far does the truck and car travel in that time?
 
I got it. Truck and car travel ~154.6m. 154.6-84.5 = ~70

Car: 154.6-70= ~ 84.6m from each other

Thanks
 

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