Kinematic Problem: Calculating Acceleration & Velocity

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SUMMARY

The discussion focuses on calculating the instantaneous acceleration vector of a car transitioning from a straight path to a curve with a radius of curvature of 2 km and an angular acceleration of 3 rad/s². The car initially travels at a velocity of 90 km/h over a straight distance of 5 km before entering a curve with a 60° angular width. Key calculations include determining tangential acceleration using the formula a_t = α * R and centripetal acceleration using a_n = v²/R. The average velocity between the straight path and the curve's midpoint is also discussed.

PREREQUISITES
  • Understanding of angular acceleration and its application in kinematics
  • Familiarity with centripetal acceleration and its calculation
  • Knowledge of basic kinematic equations for linear and angular motion
  • Ability to convert units between km/h and m/s for accurate calculations
NEXT STEPS
  • Study the derivation and application of the kinematic equations for angular motion
  • Learn how to calculate average velocity in curved motion scenarios
  • Explore the relationship between linear and angular quantities in physics
  • Practice problems involving tangential and centripetal acceleration in various contexts
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Students studying physics, particularly those focusing on kinematics, automotive engineers, and anyone interested in the dynamics of vehicles navigating curves.

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Homework Statement



A car moves from west to east with a velocity v = 90 km / h on a straight stretch of 5km, then meets a curve to the north with 60 ° angular width and radius of curvature of r = 2Km that runs with constant angular acceleration of 3 rad / (s ^ 2). calculate the instantaneous acceleration vector in mid corner and exit from the curve, calculate also the average velocity between the beginning of the straight and half of the curve and between the beginning of the straight and the 'out of the curve.



Homework Equations





The Attempt at a Solution


As for mid-corner acceleration, I calculated the tangential acceleration a_t = alpha * R * 3 = 2000 = 6000m / (s ^ 2). It remains to calculate the centripetal acceleration at mid-corner and so when the curve has angular width of 30 degrees and the car is at point P. Since a_n = v ^ 2 / R How do I calculate v_p? thanks
 
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welcome to pf!

hi vivident! welcome to pf! :smile:

(try using the X2 and X2 icons just above the Reply box :wink:)
vivident said:
Since an = v2/R How do I calculate vp?

you mean what is the speed half-way round?

just use the standard https://www.physicsforums.com/library.php?do=view_item&itemid=204" equations, with angular acceleration velocity and displacement instead of ordinary (linear) acceleration velocity and displacement :wink:
 
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hey thanks:) i did it now ;) was stuck cause numerical data are odd!
 

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