tangential and normal components of acceleration

Question

r(t)=ti+2/tj, t=3 and r(t)=t^2i+2tj, t=1 both need a tangential and normal components of acceleration.

Answer 1

I will do the first one and show procedure:

v(t) = dr/dt = i - (2/t²)j

|v| = sqrt(1+4/t⁴)

a_T = d|v|/dt = (1/2)(1+4/t⁴)^-1/2(-16/t⁵) = (-8/t⁵)/(sqrt(1+4/t⁴)

a(t) = dv/dt = (4/t³)j

|a| = 4/t³

a_N = sqrt( |a|²- a_T²) = sqrt( 16/t⁶ - 64/(t¹⁰(1 + 4/t⁴)))

Not pretty..