The position of an object at time t is given by s(t) = -9 - 5t. Find the instantaneous velocity at t = 4 by finding the derivative.

Question

The position of an object at time t is given by s(t) = -9 - 5t. Find the instantaneous velocity at t = 4 by finding the derivative.

Answer 1

Instantaneous velocity, also known as v(t) is known as the derivative of the position function s(t). In other words, v(t) is the slope of s(t) at any point t.

s(t) is given as the following:

s(t) = -9 -5t

When we calculate the derivative, we can get the following for v(t)

v(t) = s'(t) = -5

We can also look at the graph of s(t) and determine that the plot is linear with a constant slope of -5.

Therefore, the instantaneous velocity at t = 4 is -5. Note that the instantaneous velocity is always going to be -5 in this problem, regardless of the t-value we use.