# Write the Formula for Distance Traveled in nth Second

By K Balaji|Updated : November 9th, 2022

The formula for distance traveled in nth second is Snth = u + a (n - ½).

### Distance

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Step 1: It is given that

S = ut + ½ at2

Here,

S = distance traveled.

u = initial velocity.

t = time.

a = acceleration

Step 2: For the distance traveled in time n and n-1 second

Consider

u as the initial velocity

a as the acceleration

Distance traveled in n second = Sn

Using the second equation of motion,

Distance traveled in t seconds,

S = ut + ½ at2

Distance traveled in n seconds,

Sn = un + ½ an2…. (1)

Distance traveled in (n-1) seconds,

S(n-1) = u (n - 1) + ½ a (n-1)2 …. (2)

Step 3: The formula to find the distance traveled in time n and n-1 second

For nth second,

Snth = Sn - S(n-1) … (3)

Substituting values of Sn and S(n-1) from (1) and (2)

Snth = un + ½ an2 - [u (n - 1) + ½ a (n-1)2]

Simplification of the above equation

Snth = u + ½ a (2n - 1)

Snth = u + a (n - ½)

Hence, the equation for distance traveled in nth second is Snth = u + a (n - ½)

Summary:-

## Write the Formula for Distance Traveled in nth Second

The formula for distance traveled in nth second is Snth = u + a (n - ½) where u is the initial velocity, a is the acceleration and S is the distance travelled. The sum of the movement of an object is termed as the distance.

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