The distance a cart moves down a track (from rest) is proportional to the time squared. How far would a cart move down a track (from rest) in two seconds if it moves (from rest) a distance of 20 cm in one second? A) 5 cm B) 10 cm C) 20 cm D) 40 cm E) 80 cm

A car move down a track a distance of 80 cm

Letter E  80 cm

Proportional

if the distance is proportional to the time square we can express such condition writing

d = k*t²        (1)

where d is the distance t is the time and k is the constant of proportionality.

Now we must considerer that if the cart moves a distance of 20 cm in one second then by substitution in equation (1)

20 = k * (t)²        ⇒     20 = k*1   then   k = 20

The proportionality constant is K = 20

To determine how far the cart move down in 2 seconds, again by substitution in equation (1) ( but now knowing k )

d = 20*(2)²

d = 20*4

d = 80 cm

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz