Average Velocity & Instantaneous Velocity...1

[nycmathguy]

Calculus 1
Section 1.4

For part (a), just do (i).
Also, I don't understand part (b).

 

[MathLover1]

a.
find avarage velocity if

i)
t=2 and lasting 0.5seconds=> t=2.5

y=40*2.5-16(2.5)^2=0 ft/s

ii) t=2 and lasting 0.1seconds=> t=2.1

y=40*2.1-16(2.1)^2=13.44 ft/s

iii)
t=2 and lasting 0.05seconds=> t=2.05

y=40*2.05-16(2.05)^2=14.76 ft/s

iv)
t=2 and lasting 0.01seconds=> t=2.01

y=40*2.01-16(2.01)^2=15.76 ft/s



b.

Height of the function is given by

y=40t-16t^2

Require to find the instantaneous velocity when t=2 seconds

To find the velocity, find (dy/dt) first.


(dy/dt) (40t-16t^2)=40-32t

So, velocity is given by v(t)=40-32t

when t=2,

v(2)=40-32*2=40-64=-24ft/s -> instantaneous velocity

 

[nycmathguy]

a.
find avarage velocity if

i)
t=2 and lasting 0.5seconds=> t=2.5

y=40*2.5-16(2.5)^2=0 ft/s

ii) t=2 and lasting 0.1seconds=> t=2.1

y=40*2.1-16(2.1)^2=13.44 ft/s

iii)
t=2 and lasting 0.05seconds=> t=2.05

y=40*2.05-16(2.05)^2=14.76 ft/s

iv)
t=2 and lasting 0.01seconds=> t=2.01

y=40*2.01-16(2.01)^2=15.76 ft/s



b.

Height of the function is given by

y=40t-16t^2

Require to find the instantaneous velocity when t=2 seconds

To find the velocity, find (dy/dt) first.


(dy/dt) (40t-16t^2)=40-32t

So, velocity is given by v(t)=40-32t

when t=2,

v(2)=40-32*2=40-64=-24ft/s -> instantaneous velocity

Thank you. More Calculus on Sunday.