Question

A particle is moving in a circle of radius `R` and its speed is given by `v=lambdat^(2)`, where `lambda` is a constant. Find (a) radial acceleration, (b) tangential acceleration, ( c) resultant acceleration and (d) angle between acceleration and velocity.

Answer 1

`a_(c)=(v^(2)/R )=((lambdat^(2))^(2))/(R )=(lambda^(2)t^(4))/(R )`
`v=lambdat^(2)`
`a_(t)=(dv)/(dt)=2lambdat`
`a=sqrt(a_(c)^(2)+a_(t)^(2))`
`=sqrt(((lambda^(2)t^(4))/(R ))^(2)+(2lambdat)^(2))`
`tan theta=(a_(c))/(a_(t))=(((lambda^(2)t^(4))/(R )))/(2lambdat)=(lambdat^(3))/(2R)`
`theta=tan^(-1)((lambdat^(3))/(2R))`
where `theta` is the angle between acceleration and velocity.