Arturo O. answered • 05/07/18

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You need to find the unit tangent vector

**T**(t), and evaluate the dot product of**T**(t) with your acceleration vector**a**(t). That will give the tangential acceleration a_{t}(t) at time t. I assume you started out with a position vector vector**r**(t), then you found a velocity vector**v**(t) = d

**r**(t)/dt,

and then an acceleration vector

**a**(t) = d

**v**(t)/dt

If you already have d

**r**(t)/dt**,**the unit tangent vector is just**T**(t) = d

**r**(t)/dt / |d

**r**(t)/dt| =

**v**(t) / |

**v**(t)|

Then

a

_{t}(t) =**T**(t) ·**a**(t) = [**v**(t) / |**v**(t)|] ·**a**(t)Arturo O.

Yes, since you want the projection of

**a**in the direction of the unit vector**T**.
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05/08/18

Ashley H.

05/08/18