A particle moves along a path and its speed increases withtime. (a) In which of

Question

A particle moves along a path and its speed increases withtime. (a) In which of the following cases are its acceleration andvelocity vectors parallel? thepath is straight
thepath is circular
never
thepath is a parabola

(b) From the same choices, in which case are its acceleration andvelocity vectors perpendicular everywhere along the path?
thepath is straight
thepath is circular
thepath is a parabola
never

A particle moves along a path and its speed increases withtime. (a) In which of the following cases are its acceleration andvelocity vectors parallel? thepath is straight
thepath is circular
never
thepath is a parabola

(b) From the same choices, in which case are its acceleration andvelocity vectors perpendicular everywhere along the path?
thepath is straight
thepath is circular
thepath is a parabola
never

A particle moves along a path and its speed increases withtime. (a) In which of the following cases are its acceleration andvelocity vectors parallel? thepath is straight
thepath is circular
never
thepath is a parabola

(b) From the same choices, in which case are its acceleration andvelocity vectors perpendicular everywhere along the path?
thepath is straight
thepath is circular
thepath is a parabola
never

A particle moves along a path and its speed increases withtime. (a) In which of the following cases are its acceleration andvelocity vectors parallel? thepath is straight
thepath is circular
never
thepath is a parabola

(b) From the same choices, in which case are its acceleration andvelocity vectors perpendicular everywhere along the path?
thepath is straight
thepath is circular
thepath is a parabola
never

(a) In which of the following cases are its acceleration andvelocity vectors parallel? thepath is straight
thepath is circular
never
thepath is a parabola

(b) From the same choices, in which case are its acceleration andvelocity vectors perpendicular everywhere along the path?
thepath is straight
thepath is circular
thepath is a parabola
never

thepath is straight
thepath is circular
never
thepath is a parabola thepath is straight
thepath is circular
never
thepath is a parabola thepath is straight
thepath is circular
thepath is a parabola
never

thepath is straight
thepath is circular
thepath is a parabola
never

Explanation / Answer

Hey, For (a), select the path is straight, and for (b),the path is circular. Consider a velocity vectora that points only in the y-direction of an xyplane. If we want to increase the speed ofa, then we have to add to it anacceleration vector that has only y-components; otherwise, ifwe add to a an acceleration vector that hasboth x and y components, then we will be changing the directionof a as well as its speed. If we wantedto change only the direction of a, we would add toit only an acceleration vector that has x-components. Hopethis helps.  

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