derieve the distance travelled by a body moving with a uniform acceleration in a particular second.
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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) seconds
s
n
=un+1/2an
2
–[u(n−1)+1/2a(n−1)
2
]
=un+1/2an²–[un−u+1/2a(n
2
−2n+1)]
=un+1/2an
2
–[un−u+1/2an²−an+1/2a]
=un+1/2an
2
–un+u–1/2an
2
+an–1/2a
=u+an–1/2a
s
n
=u+a(n–1/2)
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