Answer each question appropriately.
-Suppose the velocity of a body moving along the s-axis is $\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 1$.
Find the body's displacement over the time interval from $t = 2$ to $t = 8$ given that $s = s _ { 0 }$ when $t = 0$.
A) 288
B) 13.6
C) 284
D) Not enough information is given.

Question

Quizplus · Accepted Answer

The displacement of the body can be found by integrating the velocity function with respect to time over the given interval. The velocity function is $v(t) = 9.8t - 1$. Integrating this from $t = 2$ to $t = 8$ gives the displacement:$$\Delta s = \int_{2}^{8} (9.8t - 1) dt = \left[ \frac{9.8}{2}t^2 - t \right]_{2}^{8} = \left( \frac{9.8}{2} \cdot 64 - 8 \right) - \left( \frac{9.8}{2} \cdot 4 - 2 \right) = 284 - (-4) = 288.$$

Answer Each Question Appropriately dsdt=9.8t−1\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 1dtds​=9.8t−1

Answer Each Question Appropriately $\frac { \mathrm { ds } } { \mathrm { dt } } = 9.8 \mathrm { t } - 1$