A wheel undergoes a constant acceleration starting from rest at t=0 . The angular velocity of the wheel is 3.14 rad / s when t=2 ~s . The accelerator is abruptly ceased at t=20 ~s . The number of revolutions. wheel makes in the interval t=0 to t=40 ~s is

Step-by-step solution

( ) Given, =314 rad / s at t=2 ~s Let = constant angular acceleration Then using ₁= ₀+ t We have, aligned & & ₁ & = t & 314 & = (2) & ( ₀=0 ) & & & = 314 2 rad / s ^2 aligned Now, angle covered in 20 seconds is given by, array rlrl & & ₁= ₀ t+ 1 2 t^2 & & ₁= 1 2 t^2 & so, & ₁= 1 2 314 2 (20)^2=314 rad & At & t=20 ~s , angular speed of wheel, & ₂= ₀+ t & ₂=0+ 314 2 20 & ₂=314 rad / s array As, acceleration does not operates after t=20 ~s . So, wheel now rotates freely (with constant angular speed) upto 40 ~s . Angul