Write the Formula for Distance Travelled in nth Second (2024)

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^thseconds

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).