# How can I find the average impulsive force and the initial and final speed from a graph?

#### Chemist116

The problem is as follows:

An impulse force on the $\textrm{x-axis}$ direction acts on a body whose mass is $2\,kg$ as shown in the graph from below. Using this information assign True or False to the following statements.

I. The impulse given to the body is $+72\,Ns$.
II. The average impulse force is approximately $514\,N$.
III. The body has an initial speed of $-16\,\frac{m}{s}$ and its final speed is $+20\,\frac{m}{s}$.

$\begin{array}{ll} 1.&FFF\\ 2.&FTF\\ 3.&TFT\\ 4.&TTT\\ 5.&TTF\\ \end{array}$

I'm confused exactly on how can I tell the average impulse force and how to find the initial and final speeds from the graph. Can somebody help me with these?.

The only thing which I was able to find was that impulse is the area below the curve, which in this case will be given by:

$J=\frac{\left(14+4\right)\times 8}{2}=+72\,Ns$

But that's it where I'm stuck. Can somebody help me?.

#### skeeter

Math Team
Shouldn't the horizontal axis representing time be labeled $10^{-2} \text{ sec}$ ... ?

$\displaystyle J_{avg} = \dfrac{1}{t_f-t_0} \int_{t_0}^{t_f} F(t) \, dt$

#### Chemist116

Shouldn't the horizontal axis representing time be labeled $10^{-2} \text{ sec}$ ... ?

$\displaystyle J_{avg} = \dfrac{1}{t_f-t_0} \int_{t_0}^{t_f} F(t) \, dt$
I'm very sorry there was an error in the original graph it should had been this which is shown in the figure from below:

Thanks skeeter which spotted there was an error in the power sign from the graph.

Which by the way how should I understand the value when reading those expressions?: (Can somebody help me to clear out this doubt please?)

i.e.

$F=800\,N$

or $8=F\times 10^2$

then $F=8\times 10^{-2}$

By following the directions given in an earlier problem of similar characteristics I did this:

I. The impulse given to the body is $+72\,Ns$.

This part is true due as mentioned the impulse is found from the area in below the curve.

$J=\frac{8\left(14+4\right)}{2}=+72\,Ns$.

II. The average impulse force is approximately $514\,N$.

This part is also true due:

$\overline{\vec{F}}=m\frac{\Delta v}{\Delta t}=\frac{\Delta p}{\Delta t}=\frac{\vec{J}}{\Delta t}$

$\overline{\vec{F}}=\frac{72}{14\times 10^-2}=514.2857\,N\approx 514\,N$

III. The body has an initial speed of $-16\,\frac{m}{s}$ and its final speed is $+20\,\frac{m}{s}$.

This part is also true due:

$m\Delta v = \Delta p = \vec{J}$

$m\left(v_f-v_i\right)=\vec{J}$

$v_{f}=\frac{\vec{J}}{m}+v_{i}=\frac{72}{2}-16=20\,\frac{m}{s}$

Therefore the answer must be the fifth alternative and checks with the answers sheet.
I've just hope to be doing it right.