Answer each question appropriately.
-Suppose the velocity of a body moving along the s-axis is $\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 3$.
Find the body's displacement over the time interval from $t = 3$ to $t = 7$ given that $s = 3$ when $t = 0$.
A) 184
B) 4
C) 208
D) 39.2

Question

Quizplus · Accepted Answer

To find the displacement, we integrate the velocity function over the given time interval. The velocity function is $v(t) = 9.8t - 3$. Integrating this from $t = 3$ to $t = 7$, we get the displacement:$$\int_{3}^{7} (9.8t - 3) \, dt = \left[ \frac{9.8}{2}t^2 - 3t \right]_{3}^{7} = \left( \frac{9.8}{2} \cdot 7^2 - 3 \cdot 7 \right) - \left( \frac{9.8}{2} \cdot 3^2 - 3 \cdot 3 \right) = 184.$$So, the body's displacement over the time interval from $t = 3$ to $t = 7$ is 184 units.

Answer Each Question Appropriately dsdt=9.8t−3\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 3dtds​=9.8t−3

Answer Each Question Appropriately $\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 3$