An empty chamagne bottle is tossed from a hot air balloon It

An empty chamagne bottle is tossed from a hot air balloon. Its upward velocity is measured every second and recorded in the table below

t, seconds: 0, 1, 2, 3, 4, 5

v, ft/sec: 40, 8, -24, -56, -88, -120

-Find a formula for v in terms of t, v=f(t)

-Explain the phsical significance of the slope of your formula

Calculate and explain the physical significance of f(0)and f(t)=0

Solution

at t=0,v=40 =>(t₁,v₁)=(0,40)

t=1,v=8 =>(t₂,v₂)=(1,8)

slope=(8-40)/(1-0)=-32

equation is v-8=(-32)(t-1)

v-8=-32t+32

v=-32t+40

v=f(t)=-32t+40

phsical significance of the slope of your formula is upward velocity of chamagne bottle decreases by 32ft/s every next second

f(0)=-32*0 +40=40

phisical significance is initial velocity is 40ft/s

f(t)=0

-32t+40=0

32t=40

t=40/32

t=1.25

physical significance is velocity equals to zero at 1.25 seonds