Question

A single force with x-component F_x acts on a 2.0 kg object as it moves along the x-axis. A graph of F_x versus t is shown in FIGURE . Draw an acceleration graph (a_x versus t) for this object.

Short answer

According to Newton's Second Law of Motion, the force acting on the object is directly proportional to the acceleration of the object. The force is equal to the product of mass and acceleration of the object.

Step-by-step solution

Given information:

The mass of the object is m = 2 kg

The force is acting along the X-axis.

Force vs time graph is given.

Calculating the acceleration of the object at different forces given in the graph:

The formula to calculate the force is given by F = ma.

Therefore, the formula to calculate the acceleration of the object is given by

$a_x=\frac{F_x}{m}$

Substitute different values of forces and 2 kg for m to calculate the respective accelerations.

$$\begin{gathered} t=0,F_x=3,a_x=\frac{3}{2}=1.5m/s^2 \\ t=2,F_x=-1,a_x=\frac{-1}{2}=-0.5m/s^2 \\ t=3,F_x=-1,a_x=\frac{-1}{2}=-0.5m/s^2 \\ t=4,F_x=-1,a_x=\frac{-1}{2}=-0.5m/s^2 \end{gathered}$$

Draw the graph for acceleration vs time graph:

As calculated above, plug the values of time and acceleration in the excel sheet and draw the graph obtained.