Question

Please help me with my calc hwI am paying close attention

Answer 1

We define the variables:

• s = position of a particle in ml,

,

• t = time in h.

From the statement of the problem, we know that:

• a particle moves in a straight line,

,

• its position from the initial position is given by the function:

$s(t)=4t^2+t.$

We must find the average velocity of the particle over the time interval [1,4].

The average velocity is defined as the change in position or displacement (∆s) divided by the time interval (∆t) in which the displacement occurs.

The time interval is:

$\Delta t=t_2-t_1=4-1=3.$

The displacement is:

$\Delta s=s_2-s_1=s(t_2)-s(t_1)=s(4)-s(1)=(4\cdot4^2+4)-(4\cdot1^2+1)=68-5=63.$

Using the definition of the average velocity, we get:

$\bar{v}=\frac{\Delta s}{\Delta t}=\frac{63}{3}=21.$

Now, the units of the velocity are distance (in ml) over time (in h), so we have:

$\bar{v}=21\cdot\frac{ml}{h}.$

Answer

The average velocity of the particle in the time interval [1,4] is:

$\bar{v}=21\cdot\frac{ml}{h}.$