Question

The position equation for a particle is s(t)=sqrt(t^3+1) where s is measured in feet and t is measured in seconds. Find the acceleration of the particle at 2 seconds.

Answer 1

here we have to find the second derivative of \(s(t)\)

Answer 2

namely:
\[\huge s''\left( 2 \right)\]

Answer 3

for example the first derivative of \(s(t)\), is:
\[\Large s'\left( t \right) = \frac{3}{2}\frac{{{t^2}}}{{\sqrt {{t^3} + 1} }}\]
now, please compute the second derivative

Answer 4

I got (3 t (t^3+4))/(4 (t^3+1)^(3/2))

Answer 5

My answer is 2/3 ft/sec^2