Solve Vector Questions: Homework Statement

[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.

 

[nlightner]

Hello! It seems like you are on the right track with solving parts (a), (b), and (c) of this problem. To solve part (d), you can use the equations of motion for constant acceleration, which are:

x = x0 + v0t + 1/2at^2
y = y0 + v0t + 1/2at^2

Where x0 and y0 are the initial position coordinates (in this case, (0,0)), v0 is the initial velocity (in this case, vi), and a is the acceleration that you calculated in part (c). You can use these equations to find the coordinates (x,y) at any given time t.

As for your question about integrating (Vf-Vi) to get x(t), that would not work in this case because the acceleration is not constant. The equations of motion mentioned above are more appropriate for this problem.

I hope this helps! Let me know if you have any other questions.