Question

Need help with example #10 part a and part b if possible

Answer 1

Given data:

* The mass of the object is 0.20 kg.

* The net displacement of the particle is 20 m.

Solution:

(a). According to Newton's second law, the force acting on the particle in terms of the acceleration and mass is,

`F=ma`

where m is the mass of the object, a is the acceleration and F is the force acting on the object,

At the displacement x = 6 m, the force acting on the object is F = 4 N.

Thus, the acceleration of the object is,

`\begin{gathered} 4=0.20* a \\ a=(4)/(0.2) \\ a=(4)/((2)/(10)) \\ a=4*(10)/(2) \end{gathered}`

By simplifying,

`\begin{gathered} a=(40)/(2) \\ a=20ms^(-2) \end{gathered}`

Thus, the acceleration of the object in the given case is 20 meters per second squared.

(b). By the kinematics equation, the displacement of the object in terms of the acceleration and time is,

`x=ut+(1)/(2)at^2`

where u is the initial velocity of the object,

As the object is initially at rest, thus, the value of initial velocity is zero.

The force acting on the object remains constant till x = 12 m, thus, the value of acceleration also remains constant.

Substituting the known values,

`\begin{gathered} 12=0+(1)/(2)*20* t^2 \\ 12=10* t^2 \\ t^{}=\sqrt{(12)/(10)} \\ t=\pm_{}1.095\text{ s} \end{gathered}`

Neglecting the negative value of time,

Thus, the time taken by the object to reach 12 m displacement is 1.095 seconds.