At t = 0, a particle starts from rest at 𝓍 = 0, y = 0 and moves in the xy plane with an acceleration $\vec{a}=(4.0\hat{i}+3.0\hat{j}){\text{m/s}}^2$. Determine the 𝓍 and y components of velocity.

Let θ be the angle that the vector A makes with the +x-axis, measured counterclockwise from that axis. Find angle θ for a vector that has these components: A_x = 2.00m, A_y = −1.00 m

Vector A has y-component A_y = +9.60 m. A makes an angle of 32.0° counterclockwise from the +y-axis. (a) What is the x-component of A? (b) What is the magnitude of A?

Draw each of the following vectors. Then find its x- and y-components. F = (50.0 N, 36.9 degrees counterclockwise from the positive y-axis)

(III) You are given a vector in the xy plane that has a magnitude of 95.0 units and a y component of -60.0 units. (a) What are the two possibilities for its 𝓍 component? (b) Assuming the 𝓍 component is known to be positive, specify the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the - 𝓍 direction. 

Two vectors, ${\vec{V}}_1$ and ${\vec{V}}_2$, add to a resultant ${\vec{V}}_R={\vec{V}}_1+{\vec{V}}_2$. Describe ${\vec{V}}_1$ and ${\vec{V}}_2$ if $V_R^2=V_1^2+V_2^2$.