In two different situations, a constant force is applied to a moving object; the

Question

In two different situations, a constant force is applied to a moving object; the free body diagrams (FBD) for each case are shown below. The velocity vectors next to the FBDs correspond to the object's initial velocity, v0. Sketch a-t, v-t, and x-t graphs for each case. (The positive x axis points to the right.)

Note: Graphs are at the bottom of the question

FBD 1: http://capa.phys.dal.ca/dalphysicslib/Graphics/Gtype09/newtonfbd.1.gif

FBD 2: http://capa.phys.dal.ca/dalphysicslib/Graphics/Gtype09/newtonfbd.4.gif

Answer the following questions about the given free body diagrams given above:
For your answer, choose any of the curves from either diagram; e.g., enter ABCHI. If more than one curve applies to a question, enter the labels in alphabetical order. If none of the curves applies, enter N.

1) Which curve(s) could describe position vs. time for FBD 1?

2) Which curve could describe velocity vs. time for FBD 1?

3) Which curve could describe acceleration vs. time for FBD 2?

4) Which curve(s) could describe position vs. time for FBD 2?

Here are the graphs to choose answers from:

Explanation / Answer

let mass of the object be m.

for FBD 1:

force applied is along the same direction as that of initial velocity and it is in positive direction

acceleration=a=F/m and it is a constant value.

as F is positive, a will also be positive.

then velocity at any time t is given as:

v=initial velocity+acceleration*time

==>v=V0+a*t

as a is positive and V0 is positive, it is a linear equation.

position at any time t is given as:

x=initial position+initial velocity*time+0.5*acceleration*time^2

so it is a parabolic equation.

so for FBD 1, corresponding graphs are as below:

a-t: graph K

v-t: graph I

x-t : graph H

for FBD 2:

force applied is along the same direction as that of initial velocity and it is in negative direction

acceleration=a=F/m and it is a constant value.

as F is negative, a will also be negative.

then velocity at any time t is given as:

v=initial velocity+acceleration*time

==>v=V0+a*t

as a is negative and V0 is negative, it is a linear equation.

position at any time t is given as:

x=initial position+initial velocity*time+0.5*acceleration*time^2

so it is a parabolic equation.

so for FBD 1, corresponding graphs are as below:

a-t: graph D

v-t: graph F

x-t : graph G

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