A small piece of Styrofoam packing material is dropped from a height of 1.90 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a = g − Bv. After falling 0.400 m, the Styrofoam effectively reaches terminal speed, and then takes 5.40 s more to reach the ground.(a) What is the value of the constant B?s-1(b) What is the acceleration at t = 0?m/s2 (down)(c) What is the acceleration when the speed is 0.150 m/s?m/s2 (down)

Explanation:

If a small piece of Styrofoam packing material is dropped from a height of 1.90 m above the ground and reaches a terminal speed after falling 0.400m, the Change in distance will be 1.90m - 0.400 = 1.50m

If it takes 5.4secs fo r the Styrofoam to reach the ground, the terminal velocity will be expressed as;

Vt = change in distance/time

Vt = 1.5m/5.4s

Vt = 0.28m/s

Note that the Styrofoam reaches its final velocity when the acceleration is zero.

To get the constant value B from the equation a = g-Bv

a = 0m/s²

g = 9.81m/s²

v = 0.28m/s

Substituting the parameters into the formula.

0 = 9.81-0.28B

-9.81 = -0.28B

Divide both sides by -0.28

B = -9.81/-0.28

B = 35.04

b) at t = 0sec, the initial terminal velocity is also zero.

Substituting v = 0 into the equation to get the acceleration.

a = g-Bv

a = g-B(0)

a = g

Hence the acceleration at t =0s is equal to the acceleration due to gravity which is 9.81m/s²

c) Given speed v = 0.150m/s

g = 9.81m/s²

B = 35.04

Substituting the given data into the equation a = g-Bv

a = 9.81-35.04(0.15)

a = 9.81 - 5.26

a = 4.55m/s²

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day