Question

A body of mass 'm' begins to move under the action of time-dependent force `vec"F" = ("t"hat"i" + 2"t"^2hat"j")`N where `hat"i" and hat"j"` are unit vectors along x and y axis respectively. The power developed by the force in watt at time 't' is ______.

Options

• `("t"^3/"3m" + "3t"^3/"2m")`

• `("t"^2/"m" + "4t"^5/"3m")`

• `("t"^3/"2m" + "3t"^4/"2m")`

• `("t"^3/"2m" + "4t"^5/"3m")`

Answer 1

A body of mass 'm' begins to move under the action of time-dependent force `vec"F" = ("t"hat"i" + 2"t"^2hat"j")`N where `hat"i" and hat"j"` are unit vectors along x and y axis respectively. The power developed by the force in watt at time 't' is `underline(("t"^3/"2m" + "4t"^5/"3m"))`.

Explanation:

F = `"t"hat"i" + 2"t"^2hat"j"`

ma = `"t"hat"i" + 2"t"^2hat"j"`

m`"dv"/"dt" = "t"hat"i" + 2"t"^2hat"j"`

mv = `"t"^2/2 hat"i" + "2t"^3/3 hat"j"`

v = `"t"^2/"2m" hat"i" + "2t"^3/"3m" hat"j"`

`therefore "P" = "F"."v" = "t"^3/"2m" + "4t"^5/"3m"`