Normal and Tangential Velocity and Accelerations

When a particle goes around a curve it develops a tangential velocity and acceleration as well as a normal acceleration. To view the normal and tangential components on a curve refer to the image below.

To calculate the normal and tangential velocity and accelerations the following equations would be used.

(Eq 1)  $v_t=v=\frac{ds}{dt}$

(Eq 2)  $ a_t=\frac{dv_t}{dt}$

(Eq 3)  $a_n=\frac{v^2}{r}$

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