A uniformly accelerated particle is at x=7 m at t=1 s and x=27 m at t=3 s. If x=0 at t=0, its position at t=5 s is:
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A uniformly accelerated particle is at x=7 m at t=1 s and x=27 m at t=3 s. If x=0 at t=0, its position at t=5 s is:

G1 Physics · Accepted Answer

Use x = ut + (a/2)t². At t=1: u + a/2 = 7. At t=3: 3u + 9a/2 = 27. Three times the first equation gives 3u + 3a/2 = 21. Subtracting, 3a = 6 ⇒ a=2 m s⁻². Then u+1=7 ⇒ u=6 m s⁻¹. At t=5: x = 6(5) + (2/2)(25) = 30+25 = 55 m.