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AP® Physics C: Mechanics

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Difficult

Velocity with an Exponentially Decreasing Force

APPHMC-U1HXXW

A particular force acting in one-dimension decreases with time according to the function:
$$F(t)=F_0 { e }^{ -bt }$$

If an object of mass $m$ starts at rest and encounters this particular force, what will its velocity $v(t)$ be as a function of time?

A

$v(t)= {F_0}t$

B

$v(t)= \cfrac {{F_0}t}{ m }$

C

$v(t)= \cfrac {F_0}{ mb } { e }^{ -bt }$

D

$v(t)= \cfrac {F_0}{ mb } ( 1-{ e }^{ -bt } )$

E

$v(t)$ is undefined for this scenario.