Question

Velocity of a particle depends upon time as $v={\beta }^2$. The distance travelled by the particle is time $t$ is

• A. $\beta t^3$
• B. ${\beta }^{2}t$
• C. $\beta t^2$
• D. $\beta t$

Answer 1

The correct option is B ${\beta }^{2}t$

Velocity of a particle depends upon ,

$v={\beta }^2$. . . . . .(1)

velocity, $v=\frac{dx}{dt}$. . . . . . . . .(2)

From equation (1) and (2). we get

$\frac{dx}{dt}={\beta }^2$

$dx={\beta }^{2}dt$

Integrating both side,

$x=\int dx=\int {\beta }^{2}dt$

$x={\beta }^{2}t$

The correct option is B.