Question

A single force with x-component F_xacts on a 2.0 kg object as it

moves along the x-axis. The object’s acceleration graph (a_x versus t)

is shown in the figure. Draw a graph of F_x versus t.

Short answer

According to Newton's Second Law of motion, the force acting on the body is directly proportional to the acceleration of the body and inversely proportional to the mass of the body.

Therefore, the graph is obtained for the force-time graph.

Step-by-step solution

Given information:

The mass of the object is m = 2.0 kg.

The force with x-component F_x is acting on the object as it moves along the x-axis. The object’s acceleration graph (a_x versus t) is given.

Calculation of forces at each points:

According to Newton's Second Law, the formula to calculate the force acting on the object along X-axis is given by

$F_x=m{a}_x$

where F_x is the force, m is the mass and a_x is the acceleration along the X-axis.

Calculate the value of forces at t=0,1,2,3,4 by using the value of acceleration.

$$\begin{gathered} F_0=m{a}_0=\left(2kg\right)\left(0m/s^2\right)=0N \\ {F}_1=m{a}_1=\left(2kg\right)\left(1.5m/s^2\right)=3N \\ {F}_2=m{a}_2=\left(2kg\right)\left(3m/s^2\right)=6N \\ {F}_3=m{a}_3=\left(2kg\right)\left(0m/s^2\right)=0N \\ {F}_4=m{a}_4=\left(2kg\right)\left(0m/s^2\right)=0N \end{gathered}$$

Make a table for the data of t, a and F:

t (s)	a (m/s2)	F ( N)
0	0	0
1	1.5	3
2	3	6
3	0	0
4	0	0

Draw the graph for Force vs time.

Plug the above data into excel sheet and draw a graph between the force and time.