Question

If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1s and 2s is

Options

• `3/2 A + 7/3B`

• `A/2 + B/3`

• `3/2 A + 4B`

• 3A + 7B

Answer 1

`3/2 A + 7/3B`

Explanation:

Given, v = At + Bt²

∴ `(dx)/(dt) = At + Bt^2`

∴ x = `int_1^2 [At + Bt^2]dt`

∴ x = `[(At^2)/2 + (Bt^3)/3]_1^2`

∴ x = `A/2 (4 - 1) + B/3 (8 - 1)`

∴ x = `3/2 A + 7/3 B`