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Question

Write the formula for distance traveled in nth second.


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Solution

Step 1: Given

S=ut+12at2

Here,

S is the distance traveled.

u is the initial velocity.

t is the time.

a is the acceleration

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

Let,

Initial velocity = u

Acceleration = a

Distance traveled in n second = Sn

By the second equation of motion,

Distance traveled in t seconds,

S=ut+12at2

Distance traveled in n seconds,

Sn=un+12an2 ----- (i)

Distance traveled in (n-1) seconds,

S(n-1)=u(n-1)+12a(n-1)2 ----- (ii)

Step 3: Formula for distance traveled in n and n-1 second

To calculate the distance traveled in nth second,

Snth=Sn-S(n-1) ----- (iii)

Putting values of Sn and S(n-1) from equations (i) and (ii)

Snth=un+12an2-[u(n-1)+12a(n-1)2]

Simplifying the above equation,

Snth=u+12a(2n-1)Snth=u+a(n-12)

Therefore, the equation for distance traveled in nth second = Snth=u+a(n-12).


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