(a) find the position vector of a particle that has the given acceleration and the specified initial velocity and position. a(t) = 20t i + sin(t) j + cos(2t) k, v(0) = i, r(0) = j

Explanation:

a(t)=20t i+sin(t) j +cos(2t) k

v(t)=

=---------------eqn 1

given v(0)=i

i=

from equation 1

V(t)=----------eqn 2

now r(t)=

given r(0)=j

0i+1j+ok =

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂