ï»¿ Figure 3.23 gives theÂ x-tÂ 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. from Physics Motion in Straight Line Class 11 Manipur Board

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Figure 3.23 gives theÂ x-tÂ 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.

At t= 0.3 sec,

Negative, Negative, Positive.

At t= 1.2 sec,

Positive, Positive, Negative

At t= -1.2 sec

Negative, Positive, Positive

For simple harmonic motion (SHM) of a particle, acceleration (a) is given by,Â

aÂ = â€“ Ï‰2xÂ ; Â Ï‰ â†’ angular frequency Â  Â  Â  â€¦ (i)Â

tÂ = 0.3 sÂ

In this time interval, xÂ is negative. Thus, the slope of the position-time graphÂ will also be negative. Therefore, both position and velocity are negative.

However, using equation (i), acceleration of the particle will be positive.

tÂ = 1.2 sÂ

In this time interval, x is positive. Thus, the slope of theÂ x-tÂ graph will also be positive. Therefore, both position and velocity are positive.

However, using equation (i), acceleration of the particle comes to be negative.Â

tÂ = â€“ 1.2 sÂ

In this time interval,Â xÂ is negative. Thus, the slope of theÂ x-tÂ plot will also be negative. Since bothÂ xÂ andÂ tÂ 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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