# Kinematics: Analyzing circular motion of a particle

Edward Hillsby
Homework Statement:
A particle moves with constant acceleration and its velocity at time t :

v= (5-0.1t)i +(3+0.2t)j

1. find a, u

2. find the time t when particle is travelling in direction NE and find its speed.

3. find the distance and bearing of the particle from the starting point at that time.
Relevant Equations:
SUVAT, TRIG, Bearing

Homework Helper
Hello @Edward Hillsby, !

Apparently you know about SUVAT. Which ones in particular can be used here ?

Sure! However, there are some requirements to get help at PF. Read here

what is u anyway ?  ah ! ##v_0## !

Tip: Make a plot !

Edward Hillsby
u/initial velocity =v0, u is popular and very common in UK

SUVAT: v=u+at, r= r0+u0t+1/2 a t^2

Homework Helper
UK is using inches and still has some catching up to do

So: you know ##v = u + at## and you know ##v.\ \ ## What can be easier ?
Tip: Make a plot !

Edward Hillsby
I am not sure how to use trig for the NE direction. It is 45 degree or pi/4, slope= 1

Homework Helper
Tip: Make a plot ! All will be revealed !

berkeman
Edward Hillsby
is it vy sin 45=uy+ayt?, it does not work. What plot?

Homework Helper
is it vy sin 45=uy+ayt?, it does not work
No. ##v_y = u_y + a_y t\ \ ## and ##\ v_x = u_x + a_x t ##

I am beginnning to fear you overlook the vector character of ##\vec r, \ \vec v,\ \vec a ## ?

What plot?
v= (5-0.1t)i +(3+0.2t)j ##\ \ ## You know what the ##\ \hat\imath\ ## and ## \ \hat\jmath\ ## stand for ?
Plot ##v_y(t)## as a function of ##v_x(t)## for ##t=0, 1, ...15## s

May I also advise you to use super- and subscripts ?

Edward Hillsby
It is working. Thanks, guys from yahoo and overflow struggle to answer. I did not overlook vectors, but was to obsessed with trigs. 1 smart mathematician got similar result, using trigs: tangent, arcus tangent and got assumption pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right? I do not know what is different between ry and r_y. Thanks

Homework Helper
It is working.
Without the plot ?

1 smart mathematician got similar result
For what ?
pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right?
I don'know if it's right. But intellegible it sure isn't

Edward Hillsby
so, can angle in certain condition, here slope =1, be expressed by opposite/adjacent in right angle triangle? It mean angle = tangent??

Homework Helper
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2022 Award
so, can angle in certain condition, here slope =1, be expressed by opposite/adjacent in right angle triangle? It mean angle = tangent??
The slope is the tangent of the angle. An angle π/4 gives a slope of 1. tan(π/4)=1.
pi/4=r_y/r_x...ry=(pi_*r_x)/4...is it right?
I assume you are using rx, ry for coordinates of position.
ry=(π/4)rx would mean the position is a bit E of NE from the origin (ry<rx), so it is wrong on two counts:
1. For exactly NE you would want the coordinates equal. I.e. (ry/rx)=1=tan(π/4).
2. The condition you should be applying is that the velocity is NE.

Last edited:
Edward Hillsby
thanks