Q.
A body initially at rest is moving with uniform acceleration a. Its velocity after n second is υ . The displacement of the body in 2s is:
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ManipalManipal 2005Motion in a Straight Line
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Solution:
u=0,a (uniform acceleration), t=n v (final velocity after n seconds) v=0+an⟹v= an ⟶(1) sn (distance travelled in n seconds) =0+21an2 sn−2=21a(n−2)2
Distance travelled in least 2 seconds =sn−sn−2 =21a[n2−(n−2)2]=21a[n2−n2−4+4x]=2an−2a⟶(2)
From equation 1 and 2 x=2a(n−1) x=u2v(n−1)