A particle is moving in a straight line as `:`
`a=1m//s^(2) 0letle10`
`a=2t tgt10`
where `t` is the time and `a` is the acceleration. If initial velocity of the particla is zero then `:`

Options

A. velocity of the particle at `t=20sec` is `310m//s`
B. displacement of the particle in `t=20s` is `1483.33m`.
C. acceleration the particle at `t=15s` is `32m//s^(2)`.
D. `v-t` graph is

Answer

A, B, D

Explanation

For `t=0` to `t=10`
`V=u+at`
`V=0+(1)(10)=10m//s`/
`a=2t`
`underset(10)overset(v)intdv=2underset(10)overset(20)inttdt ....(1)`
`v-10=2|(t^(2))/(2)|_(10)^(20)`
`v-10=(20)^(2)-(10)^(2)=300`
`v=310m//s`.
`(b)` For `t=0 ` to `t=10s`.
`S=ut+(1)/(2) at^(2)`
`rArr S=(0)(10)+(1)/(2)xx1xx(10)^(2)=50m`
From `(1)`
`v-10=t^(2)-(10)^(2)`
`v=t^(2)-90`
`underset(50)overset(S)intds =underset(10)overset(20)int(t^(2)-90)dt`
`S-50=[((20)^(3))/(3)-90xx20]-[((10)^(3))/(3)-90xx10]`
`S=50+(8000)/(3)-1800-(1000)/(3)+900`
`S=50+(7000)/(3)-900`
`rArr S=1483.33 m`