Chapter 3, Problem 105A

To determine

To draw: A position-time graph and motion diagram for the given equation.

To write: A physics problem that will correlate with the given equation.

Answer to Problem 105A

A position-time graph for the given equation is shown in Figure 1.

A motion diagram is shown in Figure 2.

The problem is, “ A position of a car is given by an equation, $x=\left(35.0\text{m}/\text{s}\right)t-5.0\text{m}$ . Find the velocity of car at $t=4\sec$ and also, explain the type of motion of a car.”

Explanation of Solution

Given:

The equation describing the motion of an object is

  $x=\left(35.0\text{m}/\text{s}\right)t-5.0\text{m}$

Formula used:

The equation of motion is defined as,

  $x=mt+c$

Where,

m is the slope of equation.

c is the intercept.

Calculation:

The given equation of motion is

  $x=\left(35.0\text{m}/\text{s}\right)t-5.0\text{m}$

The slope of the equation is 35 while the intercept will lie at $-5\text{m}$ on y -axis.

Position-time graphs are used to represent the motion of an object. For the given equation the graph is shown below.

  

Figure 1

Position is marked along y -axis in meters and time is marked along x -axis in seconds. The slope of the given graph represents velocity. So, average velocity of an object can be expressed as,

  $\begin{array}{l}v=\frac{dx}{dt}\\ v=\frac{d}{dt}\left(\left(35.0\right)t-\left(5.0\right)\right)\\ v=35.0 \text{m/s}\end{array}$

Since there is no time dependence term in the above equation, so the velocity of a given object is constant and equal to $35\text{m}/\text{s}$ . Motion diagram of an object is shown below.

  

Figure 2

Every dot in the motion diagram represents the position of an object at different time. The acceleration of an object is zero, since there is no change in velocity. It is constant.

For the given equation, write the problem in such a way that it will be solved using the equation.

Consider the problem based on real-life objects,

“ A position of a car is given by an equation, $x=\left(35.0\text{m}/\text{s}\right)t-5.0\text{m}$ . Find the velocity of car at $t=4\sec$ and also, explain the type of motion of a car.”