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The displacement of a particle moving in...

The displacement of a particle moving in a straight line is described by the relation `s=6+12t-2t^(2)`. Here `s` is in metre and `t` in second. The distance covered by the particle in first `5s` is

A

20 m

B

32 m

C

24 m

D

26 m

Text Solution

Verified by Experts

The correct Answer is:
D
`upsilon=(ds)/(dt)=12-4t`
Comparing with `upsilon=u+at, u=12 ms^(-1)` and `a=-4 ms^(-2)`
Velocity will become zero at time, `0=12-4t_(0)` or `t_(0)=3 s`.
Since, the given time t = 5 s is greater than `t_(0)=3s`
`"distance" gt|"displacement"|`
Distance `d=|s_(0-t_(0))|+|s_(t-t_(0))|=(u^(2))/(2|a|)+(1)/(2)|a|(t-t_(0))^(2)`
`=((12)^(2))/(8)+(1)/(2)xx4xx(2)^(2)=26 m`
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