An engine is working at a constant power draws a load of mass m against a resistance r. Find maximum speed of load and time taken to attain half this speed.

Options

A. `t=(Pm)/(8r^2)`
B. `t=(Pm)/(8r)`
C. `t=(Pm)/(r^2)`
D. `t=(Pm)/(9r^2)`

Answer

A

Explanation

`f=P/V`
At the time of maximum velocity f=r,i.e,
`implies` net force onload = 0
`implies r=(P)/(V_("max"))impliesV_("max")=P/r`
`F=P/v`
`m.(dv)/(dt)=P/v`
`overset(r//2r)underset(eta)(int)v.dv=(P/moverset(t)underset(0)(int)dt)`
`1/2((P)/(2r))^2=(Pt)/(m)`
`t=(Pm)/(8r^2)`