A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plane is $\theta$ radians. The distance (in meters) the ball bearing rolls in $t$ seconds is $s ( t ) = 4.1 ( \sin \theta ) t ^ { 2 }$ Determine the speed of the ball bearing after $t$ seconds.
A) speed: $5.1 ( \sin \theta ) t ^ { 2 }$ meters per second
B) speed: $( \sin \theta ) t ^ { 2 }$ meters per second
C) speed: $8.2 ( \sin \theta ) t$ meters per second
D) speed: $8.2 ( \cos \theta ) t$ meters per second
E) speed: $4.1 ( \sin \theta ) t ^ { 2 }$ meters per second

Question

Quizplus · Accepted Answer

The speed of the ball bearing after $t$ seconds is found by differentiating the distance function $s(t) = 4.1(\sin\theta)t^2$ with respect to $t$, which gives $s'(t) = 8.2(\sin\theta)t$.

A Ball Bearing Is Placed on an Inclined Plane and Begins