Write the Formula for Distance Traveled in nth Second

The formula for distance traveled in nth second is S_nth = 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 = S_n

Using the second equation of motion,

Distance traveled in t seconds,

S = ut + ½ at²

Distance traveled in n seconds,

S_n = 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,

S_nth = S_n – S_(n-1) … (3)

Substituting values of S_n and S_(n-1) from (1) and (2)

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

Simplification of the above equation

S_nth = u + ½ a (2n – 1)

S_nth = u + a (n – ½)

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