Fewpal
0 votes
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in Kinematics by (15 points)

A small ball is moving on the flat surface (without rotation) such that its position is given by:

where ex and ey are two unit vectors along the axis x and y. 

How can ı find the angle between velocity v(t) and the acceleration a(t) as t = 1?

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1 Answer

+1 vote
by (10.2k points)
edited by

Given that the position vector of the moing ball at t th instant is given by

r(t)= t.exsin(t).e​​​​​y

Differentiating wrt t we get velocity vector 

v(t)= r'(t)= 1.ex-cos(t).e​​​​​​y

Hence the angle of velocity vector  with the positive direction of x axis at t=1 is in 4th quadrant and the angle of inclination is 

tan^-1cos(1)

Now the accleration at t th instant is

a(t)=v'(t)=sin(t).e​​​​​​​​​​y

Hence acceleration vector is directed towards +ve direction of y axis .

So angle beween accleration and velocity vector at t=1 is given by

π/2+tan^-1cos(1)

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