Q.20:- Figure 3.23 gives the *x-t* plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.

**Answer:-**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* = – ω^{2}*x* ω → 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.