Question

Exercise 1. The acceleration a mass point is constant ,a= 6i + 4j ,where the unit of a is m/s2 .Its velocity is 0 at t = 0 and its initial position vector r0 = 10m .Calculate

(1)the velocity and position vector at any time

(2)the trajectory equation of the mass point on the Oxy plane

Answer 1

a) $\vec{v}=\int{\vec{a}dt}\to \vec{v}=6t\vec{i}+4t\vec{j}$

$\vec{r}=\int{\vec{v}}dt\to \vec{r}=3t^2\vec{i}+2t^2\vec{j}+10\vec{z}$

b) $x=3t^2$ and $y=2t^2$ $\to t^2=x/3$

$y=2\cdot\frac{x}{3}=\frac{2}{3}x$ . The trajectory equation $y=\frac{2}{3}x$ .