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?
a) 45°
b) 90°
c) 135°
d) 0°

Answer 1

Answer - θ = 135°

Explanation -

Tangential acceleration of body is given -

at = 5 m/s^2

Centripetal acceleration of body is -

ac = v^2 / r

ac = 20^2 / 80

ac = 5 m/s^2

Angle of resultant acceleration vector with radius,

tanθ1 = ac / at

tanθ1 = 5/5

tanθ1 = 1

θ1 = arctan(1)

θ1 = 45°

We know that velocity vector is perpendicular to radius at any instant of time.

θ2 = 90°

Hence, angle between acceleration and velocity is

θ = θ1 + θ2

θ = 45° + 90°

θ = 135°

Therefore, angle between acceleration and velocity of the body is 135°.

Answer 2

Answer:

135°

Explanation:

tangential acceleration= 5m/s^2

centripetal acceleration=v^2/r

ac= 20^2/80

= 400/80

=5m/s^2

tan anlge1= 5/5=1

tan anlge1=45°

we know velocity vector is perpendicular to acceleration = 90°

angle. made by its acceleration with its velocity is =90+45° = 135°