In the equation x = `Ka^(m)t^(n)` where K is a dimensionless constant t is time and x and a are position coordinates and acceleration of a body respectively. What are the values of m and n ?

Differentiate a^(x) w.r.t. x, where a is a positive constant.

In the expansion of (1+x)^(m+n) , where m & n are +ve integers, prove that the coefficients of x^m and x^n are equal.

A moving particle has an acceleration a = -bx, where b is a positive constant and x is the distance of the particle from the equilibrium position. What is the time period of oscillation of the particle?

A particle of mass m accelerating uniformly has velocity v at time t_1 . What is work done in time t?

If in the expansion of (1+ x )^(m) (1-x) ^(n) the coefficient of x and x ^(2) are 3 and (-6) respectively, then the value of n is-

If in the expansion of (1+x)^(m)(1-x)^(n) the coefficients of xandx^(2) are 3 (-6) respectively then , find the value of m .

The equation x= A sin omega t gives the relation between the time t and the corresponding displacement x of a moving particle where A and omega are constant. Prove that the acceleration of the particle is proportional to its displacement and is directed opposite to it.

The equation of an SHM is x=8 sin omega t + 15 cos omega t , where x is displacement and t is time . The amplitude will be