If a car has an $x$-acceleration of $a_{x}(t)=-b t+c$, and its initial $x$-velocity at time $t=0$ is $v_{x}(0)=v_{0}$, which function below best describes $v_{x}(t)$ ?
A) $-\mathrm{b}$
B) $-b+v_{0}$
C) $1 / 2 b_{t}{ }^{2}+c_{t}+v_{0}$
D) $-\mathbf{1} / \mathbf{2} b_{t}{ }^{2}+c_{t}+v_{0}$
E) $-2 b_{t}{ }^{2}+v_{0}$
F) $-1 / 2 b_{t}{ }^{2}+v_{0}$

Question

Quizplus · Accepted Answer

To find $v_x(t)$, integrate $a_x(t) = -bt + c$ with respect to $t$, and add the initial velocity $v_0$. The integration gives $-\frac{1}{2}bt^2 + ct$, and adding $v_0$ results in $-\frac{1}{2}bt^2 + ct + v_0$.

If a Car Has An xxx -Acceleration Of ax(t)=−bt+ca_{x}(t)=-b t+cax​(t)=−bt+c , and Its Initial

If a Car Has An $x$ -Acceleration Of $a_{x}(t)=-b t+c$ , and Its Initial