Question

8 multiple choice 0.5 points
reading (example-style): the position is $x(t) = -4t + 2t^2$ (meters), with t in seconds. what is the instantaneous velocity at $t = 2.5$ s?
6 m/s
-6 m/s
0 m/s
4 m/s

Explanation:

Step1: Find velocity function (derivative)

The position function is $x(t) = -4t + 2t^2$. The velocity function $v(t)$ is the derivative of $x(t)$:
$v(t) = x'(t) = \frac{d}{dt}(-4t + 2t^2) = -4 + 4t$

Step2: Substitute t=2.5 into v(t)

Substitute $t=2.5$ into the velocity function:
$v(2.5) = -4 + 4(2.5)$

Step3: Calculate the final value

$v(2.5) = -4 + 10 = 6$

Answer:

6 m/s