Velocity and acceleration of two objects

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SUMMARY

The discussion centers on calculating the maximum constant acceleration required for a car traveling at velocity v1 to avoid colliding with a truck moving at a slower constant velocity v2, positioned a distance x ahead. The initial approach involves determining the time until potential collision using the equation t = x / (v1 - v2). The conversation highlights the need to incorporate the kinematic equation V_x^2 = V_{0x}^2 + 2a_xΔx to derive the necessary acceleration. The key takeaway is that the relationship between v1 and v2 must be established to determine if the car needs to accelerate or decelerate to prevent a collision.

PREREQUISITES
  • Understanding of kinematic equations, specifically V_x^2 = V_{0x}^2 + 2a_xΔx
  • Knowledge of basic physics concepts such as velocity, acceleration, and distance
  • Ability to manipulate algebraic equations to solve for unknowns
  • Familiarity with the concept of relative motion between two objects
NEXT STEPS
  • Study the derivation and application of kinematic equations in collision scenarios
  • Learn about relative velocity and its implications in motion analysis
  • Explore real-world applications of acceleration calculations in automotive safety
  • Investigate advanced topics such as braking distance and stopping time in vehicles
USEFUL FOR

Students studying physics, automotive engineers, and anyone interested in understanding motion dynamics and collision avoidance strategies.

strigner
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Homework Statement


A car is traveling on cruise control at velocity v1. Ahead on the road, a distance x away, a truck is traveling at a slower constant velocity v2. What is the maximum constant acceleration the car needs to avoid hitting the truck?



Homework Equations



The Attempt at a Solution



The only thing I could think of solving was the time when they would collide. So I wrote like this:

v2*t + x = v1*t

x = t(v1 - v2)

t= x/(v1-v2)

I'm not sure if this is the right way to start the problem and if it is I don't know where I can go with this.
 
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there is one equation you are missing,

V_x^2=V_{0x}^2+2a_x\triangle x

you can derive it from the equation of the position of a particle:
\triangle x = v_{0x}t+1/2at^2

and the velocity of a particle

V=V_{0x}+at

Solve the velocity equation for t, plug it into the equation for the position of a particle and you get that equation.

Back to the problem:

right now say neither car/truck accelerated/decelerated, will they hit each other?
try and determine some relationship between v1 and v2, what words does the problem use that gives you some relationship between v1 and v2?

The car will be going from velocity v1 to what? what velocity will it need at least to not hit the truck?
Once you have that use the equation to determine the acceleration that will be needed for the car. and be sure to make sure you have the sign right, will the car accelerate? or decelerate?
 

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