Prove the relation, `s_t=u + at - 1/2 a.`

(a) Write a equation of motion in different states and derive the relation : s=u+(1)/(2)a(2t-1) Where, s is the distance covered in t^("th") second, u is initial velocity and a is uniform acceleration.

The angular position of a point over a rotating flywheel is changing according to the relation, theta = (2t^3 - 3t^2 - 4t - 5) radian. The angular acceleration of the flywheel at time, t = 1 s is

The position of an object moving on a straight line is defined by the relation x=t^(3)-2t^(2)-4t , where x is expressed in meter and t in second. Determine (a) the average velocity during the interval of 1 second to 4 second. (b) the velocity at t = 1 s and t = 4 s, (c) the average acceleration during the interval of 1 second to 4 second. (d) the acceleration at t = 4 s and t = 1 s.

Chek the correctness of the relation, S_(nth) = u +(a)/(2)(2n -1), where u is initial velocity, a is acceleratin and S_(nth) is the distance travelled by the body in nth second.

Can we derive the kinematic relations V= u+ at , S = ut = 1/2 at^2 and V^2 = u^2 + 2as. Explain the reason for your answer.

Equation s_t=u + at - 1/2 a does not seem dimensionally correct, why?

If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on A .

The displacement of a particle moving in a straight line is described by the relation s=6+12t-2t^(2) . Here s is in metre and t in second. The distance covered by the particle in first 5s is

The displacement of a particle moving in a straight line is described by the relation s=6+12t-2t^(2) . Here s is in metre and t in second. The distance covered by the particle in first 5s is

A body of mass 3 kg is under a constant force which causes a displacement s metre in it, given by the relation s=(1)/(3)t^(2) , where t is in seconds. Work done by the force in 2 seconds is