Kinematics – Calculating Lateral and Longitudinal Acceleration and Jerk

Question

I know how to calculate the lateral and longitudinal velocities given the velocity $v$ and heading angle $\theta$ :

$ v_{lat} = v × \ \mathrm{sin} \theta$

$v_{long} = v× \cos \theta$

But does this extend to acceleration $a$ and jerk $j$, i.e.,

$a_{lat} = a × \sin \theta$

$a_{long} = a × \cos \theta$

$j_{lat} = j × \sin \theta$

$j_{long} = j \cos \theta$

?

Thanks for your time

Answer 1

Yes, since the acceleration and jerk are both vector quantities, your equations should be ok.