Question

The velocity of a body of mass 2 kg as a function of time t is given by v(t) = 2t`hat"i" + "t"^2hat"j"`. The force acting on it, at time t = 2 s is given by ______.

Options

• `(4hat"i" + 4hat"j")"N"`

• `(2hat"i" + 2hat"j")"N"`

• `(4hat"i" + 2hat"j")"N"`

• `(4hat"i" + 8hat"j")"N"`

Answer 1

The velocity of a body of mass 2 kg as a function of time t is given by v(t) = 2t`hat"i" + "t"^2hat"j"`. The force acting on it, at time t = 2 s is given by `underline((4hat"i" + 8hat"j")"N")`.

Explanation:

Given mass m = 2 kg, v(t) = 2t`hat"i" + "t"^2hat"j"`

`therefore "a"_("t") = "dv"/"dt" = "d"/"dt" (2"t"hat"i" + "t"^2hat"j")`

`= 2hat"i" + 2 + hat"j" = 2 hat"j" +4hat"j"   (therefore "t" = 2.5)`

From F = ma = `2(2hat"i" + 4 hat"j") = 4hat"i" + 8 hat"j"`