Motion problem for constant acceleration of truck

AI Thread Summary
A truck traveling at a constant speed of 28.0 m/s approaches a stationary car that accelerates at 2.6 m/s² after pulling out into the slow lane. The problem involves calculating the time it takes for the truck to reach the car, resulting in two potential solutions: 6.32 seconds and 15.2 seconds. The correct solution is 6.32 seconds, as it is the only value that makes sense within the context of the problem. At this time, the truck maintains its speed while the car accelerates, allowing for a comparison of their velocities and distances covered. Understanding the kinematic equations is crucial for solving such motion problems accurately.
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Homework Statement


A truck travels at a constant speed of 28.0 m/s in the fast lane of a two-lane highway. It approaches a stationary car stopped a the side of the road. When the truck is still 125 m behind the car, the car pulls out into the slow lane with an acceleration of 2.6 m/s2. How long will it take the truck to reach the car? (Answer is 6.32 s)


Homework Equations


dt = dc + 125
dc = 1.3t2


The Attempt at a Solution


Okay I got the answer, but it's in quadratic form so:

1.3t2 - 28.0t + 125 =

t = 15.2 s or t = 6.32 s

How do you know which answer is the correct one?
 
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Hello? Please, I need help :frown:
 
How did you come up with your equation? You must have started from the basic kinematic equations, right?

Go back to those and try both values of t to see which one works/makes more sense.
 
Think about what this means...

At the end of t=6.32s, how fast is each vehicle moving (what are their velocities)?
What is the distance covered by each in this time interval?

What about at t=15.2s?
 

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