During the n th second of its motion a body covers a distance `s_(n)` with uniform acceleration a and initial velocity u. Show that a = `(2s_(n)-2u)/(2n-1)`.

A partical covers 35 cm, 50 cm, 89 cm distances during the third, seventh and tweIfth seconds respectiveIy of ite motion. Show that the partical is moving with a constant acceleration. Find (i) initial velocity and (ii) distance covered in 8 s by the partical.

A train, initially at station A , starts its journey and eventually stops at station B after travelling a distance s . The first part of its journey is under uniform acceleration u and the later part under uniform retardation v . Show that the time taken for the journey is sqrt(2s((1)/(u)+(1)/(v))).

A particle moves along a straight line with a retardations of av^(n+1) , where v is the velocity at time t and a is a positive constant. If at t = 0 the velocity of the particle is u, show that at = (1)/(n)((1)/(v^(n))-(1)/(u^(n))).

A particle moves in a straight line with constant acceleration, starting from a point on the line. It moves through distances a ,b,c and d, in 0. n, 2n and 3n s respectively. Show that, (i) d-a = 3(c-b) (ii) initial velocity = (4b-3a-c)/(2n) and (iii) acceleration = (c+a-2b)/(n^(2)).

The initial velocity is u and acceleration (f) is uniform. Final velocity and distance covered in the interval t are v and s respectively. Show that the velocity of the particle at half-distance is more than the velocity for half -time.

The initial velocity of a particle- is u and acceleration (f) is uniform. Final velocity and distance covered in the interval t are v and s respectively. Show that the velocity of the particle at half - distance is more than the velocity for half-time.

A particle with constant acceleration travels x m in t th second and y m in (t+n)th second. Show that the acceleration is (y-x)/(n) "m.s"^(-2) .

A small cube falls from rest along a frictionless inclined plane. If this distance travelled between times t = n -1 and t = n be s_(n) then the value of (s_(n))/(s_(n)+1) is

A particle moves along a straight line with uniform acceleration. If it travels through distances a and b, respectively in the l - th and m-th seconds then prove that the distance travelled in the n-th second is s_(n) = (a(n-m)+b(l-n))/(l-m)

A particle moves with uniform acceleration and the distance travelled in t - th second is s_(t) = 3 + 2t . Find the initial velocity of the particle .