Question

A body is moving on a circle of radius 80m with a speed 20m/s which is decreasing at the rate of 5m/s2 at an istant. What is the angle made by its acceleration with its velocity?

Answer 1

Given:         Radius(x) = 80m

      Speed (u)= 20 m s-1

  acceleration (a) =  -5 m s-2

To find the angle made by its acceleration with its velocity

 

v = u +at

v = 20 + (-5)t

v = 20 -5t  ........... (i)

 

v2 = u2 + 2as

  v2 = (20)2 + 2(-5)s         ...................(ii)

  (20 - 5t)2 = 400 -10s

400 +25t2 - 200t = 400 - 10s

{25t (t - 8) }/ 10 = -s

-{25t (t - 8) }/ 10 = s ........................(iii)

 

Here "s" is the arc.

 

Angle = arc / radius

 

Angle = s / 80

Angle = -{25t (t - 8) / 10*80

Angle = (8-t) / 32

Answer 2

centripetal acceleration = 20*20/80 = 5 m/s2 

tangential acceleration = 5 m/s2

so angle = tan-1(5/5) = 450