Write the Formula for Distance Travelled in nth Second

Answer : Now according to the science,

S = displacement

t = Time

u = Initial Velocity

a = Acceleration

Following up on the solution:

• u = Initial velocity if an object 

• a = Acceleration

• S_n = Distance travelled in n seconds from an essential position 

Calculating the second equation of motion,

Calculating the distance travelled in t second 

S = ut + ½ at²

Calculating the distance travelled in n second

S_n = un + 1/2an²

Now distance travelled in following (n – 1) seconds

S_n-1 = u (n – 1) + 1/2 a(n-1)²

Calculating the distance travelled n^th seconds 

S_n^th = S_n – S_(n-1),

S_n^th = un + ½ an² – [u (n-1) + ½ a (n-1)²].

On simplifying the mentioned equation, 

S_n^th = u + ½ a (2n-1).

S_n = u + a (n – ½).

Hence, the formula for distance travelled in nth second is given by,

S_n = u + a (n – ½).