The velocity v of a particle at time t is given by v=at + t + cb​ where a,b and c are constants. The dimensions of a, b and c are respectively :

The coordinates of a particle moving in a plane are given by x(t)= a cos (pt)and y(t)= b sin (pt) where a,b (< a)and p are positive constants of appropriate dimensions. Then,

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A charged particle of mass 5 mg and charge q = +2μC has velocity v = 2iˆ−3jˆ+4kˆ. Find out the magnetic force on the charged particle and its acceleration at this instant due to magnetic field B = 3jˆ−2kˆ,v and B are in m/s and Wb/m^2 respectively.

The position of a particle as a function of time t, is given by x(t) = at + bt^2 − ct^3 where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be