A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is $\theta = \frac { \pi } { 9 }$ radians. The distance (in meters) the ball bearing rolls in $t$ seconds is $s ( t ) = 4.9 ( \sin \theta ) t ^ { 2 }$. Determine the value of $s ^ { t } ( t )$ after one second. Round numerical values in your answer to one decimal place.
A) $s ^ { \prime } ( t ) = 3.4$
B) $s ^ { \prime } ( t ) = 1.7$
C) $s ^ { \prime } ( t ) = 4.5$
D) $s ^ { \prime } ( t ) = 5.7$
E) $s ^ { \prime } ( t ) = 2.4$

Question

Quizplus · Accepted Answer

The derivative of the distance function is the velocity function, which is given by $s ^ { \prime } ( t ) = 9.8 ( \sin \theta ) t$. Substituting $\theta = \frac { \pi } { 9 }$ and $t = 1$ gives $s ^ { \prime } ( 1 ) = 9.8 ( \sin \frac { \pi } { 9 } ) ( 1 ) \approx 3.4$.

A Ball Bearing Is Placed on an Inclined Plane and Begins