0 votes
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?

Please log in or register to answer this question.

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 


Now the accleration at t th instant is


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

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


Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.