The variation of radius of a circle with time is given by the relation `r=(2t+3)m`,where ` t ` is time in second.The rate of change of area of the circle at `t=1s` will be

The area of a circle is given by A= pi r^(2) , where r is the radius. Calculate the rate of increase of area w.r.t radius.

The position (in meters) of a particle moving on the x-axis is given by: x=2+9t +3t^(2) -t^(3) , where t is time in seconds . The distance travelled by the particle between t= 1s and t= 4s is m.

The voltage supplied to a circuit is given by V=V_(0)t^(3/2) , where t is time in second. Find the rms value of voltage for the period, t=0 to t=1s.

The area of a circle is given by A=pir^(2) , where r is the radius . Calculate the rate of increases of area w.r.t. radius.

The angular displacement of a particle is given by theta = t^3 + 2t +1 , where t is time in seconds. Its angular acceleration at t=2s is

A particle of mass 1 kg moves in a circular path of radius 1 m such that its speed varies with time as per equation v=3t^(2)m//s where time t is in seconds. The power delivered by the force acting on the paritcle at t=1s , is :-

The velocity of a particle is given by v=(2t^(2)-4t+3)m//s where t is time in seconds. Find its acceleration at t=2 second.

The position of a particle is given by the equation f(t)=t^(3)-6t^(2)+9t where t is measured in second and s in meter. Find the acceleration at time t. What is the acceleration at 4 s?

A car is moving in such a ways that the distance it covers , is given by the equations s = 4t^(2) +3t, where s, is in meters and t is in seconds . What would be the velocity and the accelerations of the car at time t=20 seconds?