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The instantaneous velocity of a particle...

The instantaneous velocity of a particle moving in a straight line is given as `v = alpha t + beta t^2`, where `alpha` and `beta` are constants. The distance travelled by the particle between 1s and 2s is :

A

`(3)/(2) alpha + (7)/( 3) beta `

B

`(alpha )/(2) + ( beta)/( 3)`

C

`(3)/(2) alpha + (7)/( 2) beta`

D

`3 alpha + 7 beta `

Text Solution

Verified by Experts

The correct Answer is:
A
` v = alpha t + beta t ^(2)`
` ( ds)/( dt) = alpha t + beta t ^(2)`
`int_( s_(1)) ^(s_(2)) ds = int_(1)^(2) ( alpha t + beta t^(2)) dt `
` S_(2) - S_(1)[ ( alpha t^(2))/(2) + (beta t^(3))/(2) ]_(1)^(2)`
As particle is not changing direction
So, distance = displacement
Distance `= [ ( alpha [ 4 - 1])/( 2) + ( beta [8 - 1])/ (3)]`
` = ( 3 alpha )/( 2) + ( 7 beta)/(3) `
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