The velocity of an object is given by $v(t)$ , and the acceleration is given by $a(t)$ .What is the relationship between the total change in v(t)over the interval 0 $\le$ t $\le$10 and a(t)?
A) $\int_{0}^{10} v(t) d t=a(10)-a(0)$
B) $\int_{0}^{10} a(t) d t=v(10)-v(0)$
C) $\int_{0}^{10} t d t=\alpha(10)-v(10)$
D) $\int_{0}^{10} v(t) d t=\int_{0}^{10} a(t) d t$

Question

Quizplus · Accepted Answer

The relationship between velocity and acceleration is that acceleration is the derivative of velocity with respect to time. Therefore, the integral of acceleration over a time interval gives the change in velocity over that interval, which is mathematically represented as $\int_{0}^{10} a(t) dt = v(10) - v(0)$.

The Velocity of an Object Is Given By v(t)v(t)v(t) , and the Acceleration Is Given By

The Velocity of an Object Is Given By $v(t)$ , and the Acceleration Is Given By