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Which of the following relations are alw...

Which of the following relations are always true ?
`vec(v)=` velocity, `vec(a)=` acceleration, `K=(1)/(2)mv^(2)=` Kinetic energy

A

`(dK)/(dt)=mvec(v).vec(a)`

B

`(d|vec(v)|)/(dt)=(vec(a).vec(v))/(|vec(v)|)`

C

`(d|vec(v)|)/(dt)=|(dvec(a))/(dt)|`

D

`|Deltavec(v)|=|underset(t_(1))overset(t_(2))intvec(a)dt|`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`vec(a)=(dvec(v))/(dt)rArr d vec(v)=vec(a)dt`
`rArr Deltavec(v)=underset(t_(1))overset(t_(2))intvec(a)dt`
Rate of change of speed `=` component of acceleration along velocity
`rArr (d|vec(v)|)/(dt)=vec(a).(vec(v))/(v)`
`K=(1)/(2)m vec(v).vec(v)rArr(dK)/(dt)=mvec(v).vec(a)`
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