Question

a particle is moving on a circular path of radius 10 cm. Its linear speed is given by v= 4t m/s. find the angle between acceleration and radius at t=2s

a) 45 degree

B) 60degree

c) theta = tan -1 5\8

d) none

Answer 1

The angle between the acceleration and radial acceleration is 45°.

(a) is correct option

Explanation:

Given that,

Radius = 10 cm

Speed = 4t

We need to calculate the angle between the acceleration and radial acceleration

Using formula of tangential acceleration

$a_{t}=\dfrac{dv}{dt}$

$a_{t}=\dfrac{d}{dt}(4t)$

$a_{t}=4\ m/s^2$

We need to calculate the angular acceleration

Using formula of angular acceleration

$a_{r}=\dfrac{v^2}{r}$

$a_{r}=\dfrac{(4t)^2}{10\times10^{-2}}$

$a_{r}=\dfrac{16t^2}{10\times10^{-2}}$

At t = 2 sec

$a_{r}=\dfrac{16\times4}{10\times10^{-2}}$

$a_{r}=640\ m/s^2$

We need to calculate the angle between the acceleration and radial acceleration

Using formula of angle

$\tan\theta=\dfrac{\sqrt{a_{t}^2+a_{r}^2}}{a_{r}}$

$\tan\theta=\dfrac{\sqrt{4^2+(640)^2}}{640}$

$\theta=\tan^{-1}(1.0)$

$\theta=45^{\circ}$

Hence, The angle between the acceleration and radial acceleration is 45°.

Learn more :

Topic : angle between acceleration and radial acceleration

https://brainly.in/question/13200595

https://brainly.in/question/12986266