What impulse does the force shown in FIGURE EX11.3 exert on a $250g$particle?

We need to find that what impulse does the force exert on a $250g$particle.

The impulse is define by

$impulse=j_x={\int }_{t_i}^{t_f}{F}_x\left(t\right)dt$

The area under the graph of force between times$t=t_{i}andt=t_f$canbe interpret geometrically.

We can also evaluate the impulse exerted on the object using this geometric interpretation. Notice that the region under the force curve between times 0 ms and 6 ms can be divided into two simple areas: a rectangle and a triangle.

height and width of a rectangle is $1000Nand2ms$. Hence the impulse from $0ms$to $2ms$is localid="1649419663107" $2000N\times ms$.

The triangle has height $1000N$and base length$4ms(6-2=4)$. Hence the impulse from $2ms$to $6ms$is

localid="1649419675437" $\frac{1}{2}\times base\times height=\frac{1}{2}\left(4ms\right)\left(1000N\right)=2000N\times ms$ The total impulse islocalid="1649418227934" $4000N\times ms$

$4000\times ms$is valid answer, $N$is the unit of impulse. so, convert this unit into the standerd approach to unit conversation : multiplying by ratios of equivalent quantities with diffrent units.

localid="1649419712818" $4000N\times ms=4000N\times \cancel{ms}\left(\frac{1s}{1000\cancel{ms}}\right)=4N\times s$