Question

A body is moving on a circle of radius 80 m with a speed 20 m/s which is decreasing at the rate 5 m/s at an instant
The angle made by its acceleration with its velocity is
(1) 45°
(2) 90°
(3) 135°
(4) 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°.