Question

A body is moving on a circle of radius 80 m with speed 20m/s which is decreasing at the rate 5 m/S2 at an instant.the angle
made by its acceleration with its velocity
​

Answer 1

Answer:

Angle, α= 135°

Explanation:

[Refer to attached image to better visualize the condition]

Given scenario is of non uniform circular motion in which the speed decreases.

Given;-

              Radius, R = 80m

           Velocity, V = 20 m/s

Tangential Acceleration, At= 5m/s²

Now;-

Let ∅ be the angle between resultant acceleration (A) of centripetal acceleration (Ac) & Tangential acceleration (At). Let 'α' denote the required angle.

Now, since the speed is decreasing in the given case, we assume that tangential acceleration is acting opposite to that of velocity.

Now, from the sides around ∅, we can say that on applying tan function on the sides, we can get our angle ∅. So;-

                          tan∅ = At/ Ac

                          tan∅ = At/ V²/R  [By formula]

                          tan∅ = 5/ 20 × 20 / 80  [As per given values]

                          tan∅ = 80 × 5/ 20 × 20

                          tan∅ = 400/400

                          tan∅ = 1

                          tan∅ = tan 45°

                                ∅ = 45°  ______(1)

Now, we also know that, in a non-uniform circular motion, centripetal acceleration is always perpendicular to the velocity.

So, we obtain;-

                        α = 90° + ∅

                         α = 90° + 45°  [From (1)]

                         α = 135°

Therefore, the angle made by acceleration and velocity is 135°.

Hope it helps! ;-))