Solveeit Logo
Login

Question

Physics Question on Motion in a straight line

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 tt= 0.3 s,1.2 s,–1.2 s.0.3 \,s, 1.2 \,s, – 1.2 \,s.
the x-t plot of a particle executing one-dimensional simple harmonic motion

Answer

Negative, Negative, Positive (at tt = 0.3  s0.3 \;s)
Positive, Positive, Negative (at tt = 1.2  s1.2 \;s)
Negative, Positive, Positive (at tt = −1.2 s- 1.2 \,s)
For simple harmonic motion (SHM) of a particle, acceleration (a) is given by the relation:
aa =–ω2×ω→angular frequency– \omega^2 \times \omega \rightarrow angular \,frequency ....(i)
tt = 0.3 s0.3 \,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.
tt = 1.2 s1.2 \,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.
tt = –1.2 s– 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.