# Find the distance travelled between $t=0$ and $t=5$ [closed]

The position vector of a particle is given as $$\vec r = \frac43 t^{3/2}\hat i - \frac{1}{2} t^2\hat j + 2 \hat k$$, $$t$$ is in seconds. Find the distance travelled between $$t = 0$$ and $$t = 5$$ seconds.

I tried it solving by putting values of $$t$$ as $$0$$ and $$5$$ seconds in the position vector, but I couldn't get the answer. (In reality, when I put $$t=5$$, the equation got really messy.) Please help me. Any help will be appreciated.

The given answer is $$22.5$$ m.

I think your position equation should be $$\vec r(t) =\left(\frac{4}{3}t^{\frac{3}{2}}\right)\hat\imath +\left(-\frac{t^{2}}{2}\right)\hat\jmath +\left(2\ \underline{t}\ \right)\hat k$$ in order to get the value listed in your spoiler.