Particle with constant acceleration: scalar product, vector product, and position

[Lord Dark]

Homework Statement

Hi guys ,, how are you all ?? ,, I have 3 questions for this day,, First :
At t = 0, a particle moving in the xy plane with constant acceleration has a speed vi =
7.5 m/s and is at the origin. At t = 3.0 s, the particle has a speed of vf = 10 m/s, with
directions of the velocities as shown in the figure

a) Calculate the scalar product of vi and vf.
b) Calculate the vector product of vi and vf.
c) What is the acceleration of the particle?
d) Find its coordinates (x,y) at any time t.

Homework Equations

The Attempt at a Solution

First i got the angle between Vf and Vi = 20 (can someone check it if it's right or wrong)
then i solved (a) and (b) using Vi*Vf cos theta and Vi*Vf sin theta ,,
solved (c) using (Vf-Vi)/t and got it as vector then change it to magnitude
but i couldn't solve (d) ,, i don't know how ,, so i need help in (d) and a question in (d) ,, should i integrate (Vf-Vi) to get x(t) ??

 

[tjkubo]

If you did (c) correctly, you should have gotten acceleration to be a vector. There are several ways to represent vectors, but regardless you should somehow use a = dv/dt = d²x/dt², a separable differential equation. A more convenient method is to manipulate one of the kinematic equations, which has already done the integrating for you.