A particle moves in a circle of radius 2 cm at a speed given by v =4t, where v is in cms ^-1 and t in seconds. The tangential acceleration at t =1s and total acceleration at t =1s are respiccitively .

Options

A. `6 cms ^(-2)and 5 cms^(-2)`
B. `4cms ^(-2)and 4sqrt(5)" " cms^(-2)`
C. `5cms ^(-2)and 5sqrt(5)" " cms^(-2)`
D. None of these

Answer

B

Explanation

Given ,radius,r=2cm
speed, v =4t
Tangential acceleration ,
`a_t =(dv)/(dt)or a_t =(d)/(dt)(4t)=4cms^(-2)`
I.e a_(t ) is constant tangential acceleration at t =1s is `4 cms^(-2) `Radial acceleration , `a_r =(v^(2))/(R) =(4t)^(2)/(R)`or`a_r =(16t^(2))/(2.0) =8.0t^2`
at t=1s ,`a^r =8.0cms^(-2)therefore " " `Total acceleration , a= `sqrt(a_t^2+a_r^2or" " a=sqrt((4)^(2)+(8)^(2))=sqrt80 therefore " "a=4sqrt(5) cms^(-2)`