Question

A particle is moving with speed v = b`sqrtx` along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0).

विकल्प

• `("b"^2τ)/4`

• `("b"^2τ)/2`

• b²τ

• `("b"^2τ)/sqrt2`

Answer 1

`bb(("b"^2τ)/2)`

Explanation:

Given, v = b`sqrtx`  or   `("d"x)/"dt"="b"x^(1//2)`

or `int_0^x x^(-1//2)"d"x=int_0^"t""bdt"`

⇒ `(x^(1//2))/(1//2)`= bt

⇒ x = `("b"^2"t"^2)/4`  

Differentiating w. r. t. time, we get

`("d"x)/"dt"=("b"^2xx2"t")/4` or v = `("b"^2τ)/2`           (t = τ)