A particle is describing uniform circular motion in the anti-clockwise sense such that its time period of revolution is T. At t = 0 the particle is observed to be at A. If [{MathJax fullWidth='false' B_1 }] be the angle between acceleration at t = T/4 and average velocity in the time interval 0 - T/4 and [{MathJax fullWidth='false' B_2 }] be the angle b/w acceleration at t = T/4 and the change in velocity in the time interval 0-T/4, then the value of [{MathJax fullWidth='false' B_1 }] and [{MathJax fullWidth='false' B_2 }] are?

Here the angle between the acceleration and average velocity is 135 degrees and angle between acceleration and difference in velocity will be 45 degrees.

Explanation:

We know that the average velocity in the time interval from 0 to  is ratio of total change in displacement to total time taken .  

 The direction of average velocity will be along the - .

 The direction of acceleration will be along the radius towards center .

 So the angle between average velocity and acceleration in given time interval will be 135 degrees .

     The direction of velocity vector is perpendicular to the position vector of given points , so the difference in velocity vectors will be in opposite direction of   - so the angle between acceleration vector and difference in velocity vector will be 45 degrees .

the bal will not change its velocity.