A particle is moving in a straight line with initial velocity U and uniform accerleration A. if the sum of distances travelled in Tth & (T+1)th second is 100 cm. Then find its velocity after T second in cm/s 

We know that the distance travelled in n^th second of uniformly accelerated motion is:

where u is the initial velocity and a the uniform acceleration of the body.

In this case given that the sum of distances travelled in T th & (T+1) th second is 100 cm

i.e.

S _T +S _T+1 =100

If the particle is moving with initial velocity U and uniform accerleration A,

Distance travelled by the particle in T^th second can be written as:

 

According to the equation of motion, we know that v = u+at

where v is the final velocity, u is the initial velocity, a the acceleration and t the time.

So comparing the equation U+AT =50 with the the equation of motion v= u+at 

we get that the final velocity of the particle at T second  = 50 cm/s