Use the definition of the derivative to find an expression for the instantaneous velocity of an object moving with rectilinear motion according to the given function relating s (in ft) and t (in s). then calculate the instantaneous velocity for the given value of t. s = 8t + 19; t=4 (simplify your answer)

The instantaneous velocity for when t = 4 is .

Step-by-step explanation:

The average rate of change of function f over the interval is given by this expression:

The average velocity is the average rate of change of distance with respect to time

The instantaneous rate of change is defined to be the result of computing the average rate of change over smaller and smaller intervals.

The derivative of f with respect to x, is the instantaneous rate of change of f with respect to x and is thus given by the formula

For any equation of motion s(t), we define what we call the instantaneous velocity at time t to be the limit of the average velocity, between t and t + Δt, as Δt approaches 0.

We know the equation of motion and we want to find the instantaneous velocity for the given value of t = 4.

Applying the definition of instantaneous velocity, we get

The instantaneous velocity for when t = 4 is .

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!