Question:

Figure 2.13 gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter13). Give the signs of position, velocity and acceleration variables of the particle at \(t\)\(0.3 \,s, 1.2 \,s, – 1.2 \,s.\)
the x-t plot of a particle executing one-dimensional simple harmonic motion

Updated On: Nov 7, 2023
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Solution and Explanation

Negative, Negative, Positive (at \(t\) = \(0.3 \;s\))
Positive, Positive, Negative (at \(t\) = \(1.2 \;s\))
Negative, Positive, Positive (at \(t\) = \(- 1.2 \,s\))
For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation: 
\(a\) =\(– \omega^2 \times \omega \rightarrow angular \,frequency\) ....(i)
\(t\) = \(0.3 \,s\)

In this time interval, x is negative. Thus, the slope of the x - t plot will also be negative.Therefore, both position and velocity are negative. However, using equation (i), acceleration of the particle will be positive.
\(t\) = \(1.2 \,s\)

In this time interval, x is positive. Thus, the slope of the x - t plot will also be positive. Therefore, both position and velocity are positive. However, using equation (i) acceleration of the particle comes to be negative.
\(t\) = \(– 1.2 \,s\) 

In this time interval, x is negative. Thus, the slope of the x - t plot will also be negative. Since both x and t are negative, the velocity comes to be positive. From equation (i), it can be inferred that the acceleration of the particle will be positive.

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Concepts Used:

Motion in a straight line

The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion. 

Types of Linear Motion:

Linear motion is also known as the Rectilinear Motion which are of two types:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.