Question

the distance, s (in feet), traveled by a car moving in a straight line is given by s(t)=4t² - 2t + 2, where t is time measured in seconds.
a. find the instantaneous velocity of the car s(t).
s(t)=

b. find the instantaneous velocity of the car at t = 3.
s(3)=

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For $s(t)=4t^{2}-2t + 2$, the derivative of $4t^{2}$ is $4\times2t^{2 - 1}=8t$, the derivative of $-2t$ is $-2\times1t^{1 - 1}=-2$, and the derivative of the constant 2 is 0. So, $s^\prime(t)=8t-2$.

Step2: Evaluate $s^\prime(t)$ at $t = 3$

Substitute $t = 3$ into $s^\prime(t)$. We get $s^\prime(3)=8\times3-2$. Then $s^\prime(3)=24 - 2=22$.

Answer:

a. $s^\prime(t)=8t - 2$
b. $s^\prime(3)=22$