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A particle moves with constant accelerat...

A particle moves with constant acceleration along a straight line streaing from rest. The percentage increase in its displacement during the 4th second compared to that in the 3rd second is

A

`33%`

B

`40%`

C

`66%`

D

`77%`

Text Solution

Verified by Experts

The correct Answer is:
B
Let a be constant acceleration of the particle. Its displacement in th second is
`D_(n)= u +(1)/(2)a(2n-1)`
Since the particle starts from rest therefore u =0
`:. D_(n)=(1)/(2)a(2n-1):. D_(3)=(1)/(2)a(2xx3-1)=(5)/(2)a`
`D_(4)=(1)/(2)a(2xx4-1)=(7)/(2)a`
% increase in its displacement
`=(D_(4)-D_(3))/(D_(3))xx100=((7)/(2)a-(5)/(2)a)/((5)/(2)a)xx100`
`(a)/((5)/(2)a)xx100=(2)/(5)xx100=40%`
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