Question

A particle is moving in a straight line under the action of a variable force which supplies power​

Answer 1

Answer:

So, what is your Question ?

Can you please rewrite this with the Question

Explanation:

Hope you understand !

Answer 2

Given:

A particle is moving in a straight line under the action of a variable force which supplies power​.

To Find:

Expression for velocity ?

Solution:

here, it is given that- particle moving in a straight line under the action of variable force which supply power.

Therefore, according to question -

$Power, P=constant ,c$

this implies-

$\[\begin{gathered} P = F \times v = c \hfill \\ \Rightarrow (ma) \times v = c \hfill \\ \Rightarrow av = c \hfill \\ \Rightarrow (\frac{{dv}}{{dt}}) \times v = c \hfill \\ \Rightarrow (v)dv = (c)dt \hfill \\ \Rightarrow \int {(v)dv = \int {(c)dt} } \hfill \\ \Rightarrow \frac{{{v^2}}}{2} = ct \hfill \\ \Rightarrow {v^2} = (2c)t \hfill \\ \Rightarrow {v^2} = (k)t \hfill \\ \Rightarrow v = \sqrt {(k)t} = \lambda \sqrt t \hfill \\ \end{gathered} \]$      where, $\lambda$ is a constant and t is time.

Hence, expression for velocity is give by;

$v=\lambda \sqrt{t}$.