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"The velocity and displacement of a uniformly accelerated body can be obtained using equations of motion." a)Derive an expression for distance covered by a uniformly accelerated body during nth second. b)A body starts moving with a speed 50m/s.Calculate the displacement made by it during the 10th second alone if its uniform acceleration is 4m/s^2.

Consider an object moving with uniform acceleration 'a' along a straight line OX with origin at O as shown in figure. Let at t = 0, the position of the object be x₀ and its velocity v0 (initial velocity). Let at t = t, the position of the object be x and its velocity v. Clearly, in time t , the displacement of the object is x - x₀ = S.
                                             

The displacement of the object in time t is given by;
                                   

If S_n and S_n-1 are the displacements of the object in n and n - 1 seconds, then displacement of the object in the n^th second is
           
Displacement,S = 50 +2(20-1) = 88 m