Kinematic Problem: Calculating Acceleration & Velocity

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A car travels east at 90 km/h for 5 km before entering a curve with a 60° angular width and a radius of 2 km, experiencing a constant angular acceleration of 3 rad/s². The discussion focuses on calculating the instantaneous acceleration vector at mid-corner and at the exit of the curve, as well as the average velocity from the start to halfway through the curve and from the start to the exit. The user calculated the tangential acceleration but needed assistance with centripetal acceleration and determining the speed at the midpoint of the curve. Guidance was provided to use standard equations for angular motion to find the necessary values. The user successfully resolved their confusion regarding the calculations.
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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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