Question

Derive formula for distance covered by the particle in the nth second.​

Answer 1

Answer:

Consider a particle moving with uniform acceleration ‘a’.Let u be the initial velocity of the particle.

Consider a particle moving with uniform acceleration ‘a’.Let u be the initial velocity of the particle.Distance travelled during nth second = Distance travelled in ‘n’ seconds – Distance travelled in (n-1)

sn = $un + \frac{1}{2} {an}^{2} (u(n - 1) + \frac{1}{2} a( {n - 1)}^{2} )$

= $un + \frac{1}{2} {an}^{2} - (un - u + \frac{1}{2} a( {n}^{2} - 2n + 1))$

= $un + \frac{1}{2} {an}^{2} - un + u - \frac{1}{2} {an}^{2} + an - \frac{1}{2} a$

= $u + an - \frac{1}{2} a$

======> $sn = u + a( n - \frac{1}{2} )$

Explanation:

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