Velocity of a particle is given by v = (3t ^(2) +2t) m/s. Find its average velocity between t = 0 to t=3s and also find its acceleration at t = 3s. Motion of the particle is in one dimension.

Velocity of a particle is given by v = (3t ^(2) +2t) m/s. Find its ave

1.	Velocity of a particle is given by v = (3t ^(2) +2t) m/s. Find its average velocity between t = 0 to t=3s and also find its acceleration at t = 3s. Motion of the particle is in one dimension.
Answer» `11 m /s, 10 (m)/(s ^(2))` `12 (m)/(s), 20 (m)/(s ^(2))` `11 (m)/(s) , 20 (m)/(s^(2))` None of the given Solution :`v = (3t ^(2) + 2t)` `therefore int v dx = int (3t ^(2) + 2r ) dt` `therefore x = 3 (t ^(3))/(3) + 2 (t ^(2))/( 2) = t ^(3) + t ^(2)` At `t =0` TIME ,` x _(0) = (0) ^(2) + (0) ^(2) =0` At t =3 time, `x _(3) = (3) ^(2) + (3) ^(2) = 36 m` `therefore` Average velocity `= (x _(3) -x _(0))/(3-0)=(36-0)/(3-0)` `=12 MS ^(-1)` Acceleration of PARTICLE, `a = (dv)/(dt) = (d)/(dt) (3t ^(2) + 2t) = 6T +2` Put `t =3s,` `a=6(3) +2=20 ms ^(-2)`