Kinematic Problem: Calculating Acceleration & Velocity

[vivident]

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

 

[tiny-tim]

welcome to pf!

hi vivident! welcome to pf!

(try using the X² and X₂ icons just above the Reply box )

Since a_n = v²/R How do I calculate v_p?

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

 

[vivident]

hey thanks:) i did it now ;) was stuck cause numerical data are odd!