The position of one particle is given by s(t) = `V_0alpha[1+e^-(alphat)]`. Find out the dimension of `alpha`.

Find out the dimension of mu_0 in_ 0 .

The instantaneous position of a particle is given by S(t) = V_(0) (1 - e^(-at))//a , where a and V_(0) are constants and a gt 0 . What are the dimensions of a and V_(0) ?

The velocity of a particle (v) at an instant 't' is given by v = at + bt^(2) , the dimension of b is

If position of a particle at instant t is given by x = t^(4) find acceleration of the particle.

The velocity V of a particle at time t is given by V = at + b/(t+c) . The dimensions of a, b and c are respectively--------.

Find the general solution of the equation sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x - alpha) , given sin alpha ne 0 .

The effeciency of a machine is given by, E=(tan theta)/(tan(theta+alpha)) where alpha is constant. Prove that, E is maximum at theta=(pi)/(4)-(alpha)/(2) and its maximum value is (1-sin alpha)/(1+sin alpha) .