The equation for a wave travelling in x direction on a string is given as y=10sin(πt−0.5x), where y and x are in m and time(t) in sec. Find the acceleration of a particle at x=πm at time t=1sec.
A
−10πm/s2
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B
−10π2m/s2
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C
5πm/s2
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D
−5πm/s2
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Solution
The correct option is B−10π2m/s2 We know,
Velocity of particle vP=∂y∂t=10πcos(πt−0.5x)
Similarly, acceleration of particle can be obtained by partial differentiation of velocity w.r.t time (keeping x constant). ⇒aP=∂vP∂t ⇒aP=π×−10πsin(πt−0.5x) ⇒aP=−10π2sin(πt−0.5x)
substituting x=πm&t=1sec in above equation we get, aP=−10π2sin(π−0.5π) aP=−10π2sinπ2 ∴aP=−10π2m/s2