How Long Will it Take Me to Catch The Bus?

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SUMMARY

Lisa is attempting to catch a bus that is accelerating at 1.10 m/s² while she runs at a constant speed of 5.05 m/s from an initial distance of 11 meters behind the bus. To determine when and where Lisa will catch the bus, one must set up equations based on their respective distances traveled over time. The bus starts from rest, and the solution involves solving for time (t) and subsequently calculating the distance at which they meet.

PREREQUISITES
  • Understanding of kinematic equations, specifically DeltaX = v₀t + 1/2at²
  • Basic algebra for solving equations
  • Concept of relative motion in physics
  • Knowledge of acceleration and constant speed dynamics
NEXT STEPS
  • Study the kinematic equations in detail, focusing on motion with constant acceleration
  • Learn how to set up and solve systems of equations in physics problems
  • Explore relative motion concepts to better understand interactions between moving objects
  • Practice similar problems involving one object accelerating and another moving at constant speed
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Students studying physics, particularly those focusing on kinematics, as well as educators looking for examples of motion problems involving acceleration and relative speed.

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Homework Statement



Lisa is late for the school bus! (Oh - no) As Otto is pulling away with a constant acceleration of 1.10 m/s/s. Lisa is 11m away and running at a constant speed of 5.05 m/s..

When will Lisa catch the bus?

Where will Lisa catch the bus using the bus's initial position as the referance point?


Homework Equations



DeltaX= volt+1/2a(t)sqrd


The Attempt at a Solution



Honestly I have sat here thinking for about 30 minutes... any insight on how to start would be great... (I don't just want the answer)
 
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Hi bleedblue1234

I think the initial speed of the bus is zero. If I interpret the question correctly, it will be like this :

Assume that Lisa catches the bus at point X after both of them move for t seconds. At that time, the bus will travel distance d and Lisa will travel distance 11 + d.
Now set up two equations and solve for t and use the value of t to find where Lisa will catch the bus. :smile:
 

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