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A particle starts with an initial veloci...

A particle starts with an initial velocity `3.0 m s^(-1)` along the positive `x-`direction and it accelerates uniformly at the rate of `0.60 m s^(-2)` .(a) Find the distance traveled by it in the first three seconds. (b) Hew much time does it take to reach the velocity `9.0 m//s` (c) How much distance will it cover in reaching the velocity `9.0 m s^(-1)` ?

Text Solution

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Here, `u=3. 0ms^(-1) , a= 6 ms^(-2)`
(a) We have to calculate (S) when `t=3 s`
`S=ut + 1/2 at^(2) =3.0 xx 1/2 xx 6 xx 3^(2) =9.0 +27 =36 m`
(b) We have to calulate (t) when `v =9.0 m//s. As `v=u+ at, so t =(v-u)//a =(9-3 )//6 =1 s`
(c ) Here, `S =?, v=9.0 ms^(-2) , As `v^(2) =u^(2) +2 aS`
so `S=((v^(2)-u^(2)0)/(2a) =((9.0)^(2) -(3.0)^(2))/(2xx 6) =(81-9)/(1.20 =(72)/(12) =6 m`.
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