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A particle travels in a straight line, such that for a short time 2s≤t≤6s, its motion is described by v=(4/a) m/s, where a is in m/s 2 . If v =8m/s when t = 2s, determine the particle's acceleration when t = 4s.
Asked by varmaakshay2020 | 13 Jun, 2022, 11:43: AM
Velocity v = ( 4/a ) m /s  ....................... (1)

where a = acceleration in m/s2

Hence we get , v × a =  v × (dv/dt) = 4

v × dv = 4 dt

By integrating both sides of above expression, we get

(1/2) v2 = 4 t + C  ........................(2)

where C is integration constant

If we apply initial condition , at t = 2 , v = 8 to above expression, we get C = 24

hence ,  eqn.(2) is rewritten as  v2 = 8t + 48  .................... (3)

velocity at t = 4 s is calculated from eqn.(3) as ,  v = 4√5 m/s

Acceleration at t = 4 is calculated from eqn.91) as ,  a = 4 / ( 4√5 ) = ( 1 / √5 ) m/s2
Answered by Thiyagarajan K | 13 Jun, 2022, 12:34: PM

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