If the position of an object moving along a straight line is given by $s ( t ) = t ^ { 3 } - 7 t ^ { 2 } + 8 t$ at time t, find the object's velocity as a function of time.
A) $v ( t ) = 3 t ^ { 2 } - 7 t + 8$
B) $v ( t ) = t ^ { 2 } - 14 t$
C) $v ( t ) = t ^ { 2 } - 7 t + 8$
D) $v ( t ) = 3 t ^ { 2 } - 14 t + 8$

Question

Quizplus · Accepted Answer

The velocity of an object is the derivative of its position with respect to time. Differentiating $s(t) = t^3 - 7t^2 + 8t$ with respect to $t$ gives $v(t) = 3t^2 - 14t + 8$.

If the Position of an Object Moving Along a Straight s(t)=t3−7t2+8ts ( t ) = t ^ { 3 } - 7 t ^ { 2 } + 8 ts(t)=t3−7t2+8t

If the Position of an Object Moving Along a Straight $s ( t ) = t ^ { 3 } - 7 t ^ { 2 } + 8 t$