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Motion in Straight Line

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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.


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, 

a = – ω2x ;  ω → angular frequency       … (i) 

t = 0.3 s 

In this time interval, x is negative. Thus, the slope of the position-time graph 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-graph 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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