Question

A$2.0kg$object initially at rest at the origin is subjected to the time-varying force shown in the figure. What is the object’s velocity at$t=4s$?

Short answer

The velocity at$\text{t =}4s\text{is}9m/s.$

Step-by-step solution

Given information.

Mass (m) = $2kg,$time (t) = $4s$, force vs. time graph :

Calculation.

For velocity at a given time :

$v\left(t\right)=v_o+\text{area under the curve from 0 to 3s.}$

Area under the curve = Area of the triangle.

$=\frac{1}{2}\times B\times H.$

Continuation of calculation.

Now,

$$\begin{gathered} v\left(t\right)=v_o+\text{area under the curve from 0 to 3s.} \\ =0+\frac{1}{2}\left(6N\right)\left(3s\right). \\ =9\mathrm{m}/\mathrm{s}. \end{gathered}$$

Area between the $3s\text{to}4s$is zero,

So, $v(t=4\mathrm{s})=9\mathrm{m}/\mathrm{s}.$

Final answer.

The object's velocity at$\text{t =}4s\text{is}9m/s.$