The current in a resistor varies with time according to the equation `I=5A+2As^-1t` Calculate how many colulomb pass through the cross section of the resistor in the time interval between t = 2s and t = 5s.

The acceleration of a particle starting from rest varies with time according to the relation a=-sw^2 sin wt The displacement of the particle at time 't' will be

The magnetic flux linking a coil perpendicular to its plane is varying according to the relation phi = (5t^3 + 4t^2 + 2t-6) Wb. Calculate induced current through the coil at t = 2s if the resistance of the coil I s 3Omega .