When Does Runner B Pass Runner A?

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SUMMARY

In the discussion titled "When Does Runner B Pass Runner A?", it is established that Runner A, running at a constant speed of 6.0 m/s for 10 seconds, covers a distance of 60 meters. In contrast, Runner B accelerates from 4.0 m/s to 10.0 m/s over the same duration, resulting in a distance of 70 meters. To determine the exact moment Runner B overtakes Runner A, the equation for distance must be set equal, leading to the need for a formula that incorporates Runner B's changing velocity.

PREREQUISITES
  • Understanding of basic kinematics, including distance and velocity equations.
  • Familiarity with the concepts of constant speed and uniform acceleration.
  • Knowledge of how to manipulate equations to solve for unknown variables.
  • Ability to interpret and apply mathematical formulas in physics contexts.
NEXT STEPS
  • Study the kinematic equations for uniformly accelerated motion.
  • Learn how to derive equations for distance covered by an object with changing velocity.
  • Explore graphical representations of motion to visualize when one object overtakes another.
  • Practice solving similar problems involving relative motion and acceleration.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding concepts of motion, particularly in scenarios involving acceleration and relative speed.

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Homework Statement


Runner A runs at 6.0m/s for 10s. Runner B accelerates from 4.0 m/s to 10.0 m/s steadily in 10s. How far does Runner A go in 10s? How far does Runner B go in 10s? At what time did Runner B pass Runner A if they were both at the same position at t=0?

Homework Equations


d= v*t, d = 1/2(v1+v2)*t

The Attempt at a Solution



Runner A:
d = v*t
d = (6.0m/s)(10s)
d = 60m

Runner B:
d = 1/2(v1+v2)*t
d = 1/2(4m/s+10m/s)*(10s)
d = 1/2(14m/s)*(10s)
d= 70m

so therefore at 10s, Runner B has already surpassed Runner A by 10m. But how would you find when Runner B passed Runner A?


Many thanks.
 
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Do you see that you want to find t such that vt = ½(v1+v2)t? How can you write v2 in terms of t?
 
Tedjn said:
Do you see that you want to find t such that vt = ½(v1+v2)t? How can you write v2 in terms of t?

im sorry. i don't understand..
 

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