Thread: Tangential Accel and Normal Accel.

1. The position of a particle in motion in the plane at time is
At time , determine the following:
(a) The speed of the particle
8.85663593
(b) The unit tangent vector to
.9936053 .112909688

(c) The tangential acceleration
?
(d) The normal acceleration
?
I figured out the speed and T(t) but i have no idea how to find the aT and aN. Please help out.

you're answer to b is correct but it is T(0) not T(t)

This is not going to be very clean anyway you approach it--so have a cup of coffee and a cigarette

if s is the speed = |v|


It might be easiest to compute aN = k(ds/dt)^2

then aT = sqrt( |a|^2 - aN^2)

Where k = |T'|/|r'|



Normally you can compute the components by :

if s is the speed = |v|

Then aT = d^2s/dt^2

Without having to compute the curvature you can compute

aN = sqrt( |a|^2 - aT^2)

where a = (8.8)^2 e^(8.8t) i + e^t j

However for this problem d^2s/dt^2 is very cumbersome