Question

question 7 · 1 point a particle travels along a horizontal line according to the function s(t)=t^4 - 7t^3 - 2t^2 + 2 where t is measured in seconds and s is measured in feet. find the acceleration function a(t). provide your answer below: a(t)=□

Explanation:

Step1: Recall the relationship between position, velocity and acceleration

Acceleration is the second - derivative of position. First, find the velocity function $v(t)$ by differentiating the position function $s(t)=t^{4}-7t^{3}-2t^{2}+2$.

Step2: Differentiate $s(t)$ to get $v(t)$

Using the power rule $\frac{d}{dt}(t^{n}) = nt^{n - 1}$, we have $v(t)=\frac{d}{dt}(t^{4}-7t^{3}-2t^{2}+2)=4t^{3}-21t^{2}-4t$.

Step3: Differentiate $v(t)$ to get $a(t)$

Differentiate $v(t)=4t^{3}-21t^{2}-4t$ with respect to $t$ again using the power rule. So $a(t)=\frac{d}{dt}(4t^{3}-21t^{2}-4t)=12t^{2}-42t - 4$.

Answer:

$12t^{2}-42t - 4$