Question #334228

Q.4) If an object starts out at rest and falls a distance of s feet in t seconds, then physical laws imply that s = 16t². Find ∆s/∆t as t changes from t0 to t0 + ∆t.



Use the result to find ∆s/∆t as t changes from:



(a) 3 to 3.5, (b) 3 to 3.2, and (c) 3 to 3.1

1
Expert's answer
2022-04-27T17:08:36-0400
Δs=s(t0+Δt)s(t0)\Delta s=s(t_0+\Delta t)-s(t_0)

=16(t0+Δt)216(t0)2=16(t_0+\Delta t)^2-16(t_0)^2

=32t0Δt+16(Δt)2=32t_0\Delta t+16(\Delta t)^2

Δs/Δt=32t0+16Δt\Delta s/\Delta t=32t_0+16\Delta t

(a) t0=3,Δt=3.53=0.5t_0=3 , \Delta t=3.5-3=0.5


Δs/Δt=32(3)+16(0.5)=104\Delta s/\Delta t=32(3)+16(0.5)=104

(b) t0=3,Δt=3.23=0.2t_0=3 , \Delta t=3.2-3=0.2


Δs/Δt=32(3)+16(0.2)=99.2\Delta s/\Delta t=32(3)+16(0.2)=99.2

(c) t0=3,Δt=3.13=0.1t_0=3 , \Delta t=3.1-3=0.1


Δs/Δt=32(3)+16(0.1)=97.6\Delta s/\Delta t=32(3)+16(0.1)=97.6

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