Check the correctness of following equation by the method of dimensions :
`S=ut+(1)/(2)at^(2)` .
where S is the distance covered bu a body in time t, having initial velocity u and acceleration a.

Check the accuracy of the relation s = ut + (1)/(2)at^(2) where s is the distance travelled by the with uniform acceleration a in time t and having initial velocity u.

If the distance s travelled by a body in time t is given by s = a/t + bt^2 then the acceleration equals

In the equation of motion, S=ut+1/2 at^(2), s stands for

If the distance s covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

If the distance s travelled by a particle in time t is s=a sin t +b cos 2t , then the acceleration at t=0 is

Check the correctness of the equation, FS=(1)/(2)mv^(2)-(1)/(2)mu^(2) where F is the force acting on a body of mass m and S is the distacne moved by the body when its velocity changes from u to v.

Whether a given relation / formula is correct or not can be checked on the basis of the principle of homogeneity of dimensions. According to this principle, only that formula is correct, in which the dimensions of the various terms on one side of the relation are equal to the respective dimensions of these terms on the other side of the relation. With the help of the compreshension given above, choose the most appropriate alternative for each of the following questions : The distance travelledl by a body in nth second is given by S_(nth) = u + (a)/(2) (2n-1) where u is initial velocity and a is acceleration. The dimensions of S_(nth) are

Assertion : In the equation, s=u+at-(1)/(2)a where, s is the distance travelled by uniformly accelerated body in tth second. Reason : The above equation is dimensionally incorrect.

In S=ut+(1)/(2)at^(2) , S=96,t=8 and a=2 , find u.

The displacement of a body is given by 2 s= g t^(2) where g is a constant. The velocity of the body at any time t is :