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The accleration of a particle moving in a straight line varies with displacement as a =2s, velocity of a particle is zero at zero displacement. Find corresponding velocity-displacement equation.
Asked by acv27joy | 19 May, 2018, 07:06: PM
acceleration      dv/dt  = 2×s , where s is displacement and v is speed  at time t;

Let us assume time dependent functional form of displacement s is of the following form

s = ekt ................................(1)

ds/dt = k×ekt = k×s ........................(2)

d2s/dt2  = k2×ekt = k2×s.....................(3)

but given equation is d2s/dt2  = 2×s .....................(4)

from eqn.(3) and eqn.(4), we can write k = √2 ...........(5)

velocity-displacement relation from eqn.(2) is given by

v = √2×s  .....................(6)

eqn.(6) satisfies the given condition v= 0 when s = 0
Answered by Thiyagarajan K | 20 May, 2018, 11:07: AM

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