Question

A) Sketch the position vs. time graph for the following motion. Starting at 0.5m from the detector, you moved away at a constant velocity of 3 m/s for 2 seconds, then stood still for 1 second and then walked toward the detector for 1 second at a velocity of 4m/s after which you stood still for 3 seconds.

B) sketch the velocity vs. time graph for the above description.

Answer 1

1) At t = 0 sec, x= 0.5m

∴

2) From t=0 sec to t=2sec,

Now, you move with velocity of away from the detector.

∴

This is the equation of line parallel to horizontal axis at a distance of 3 units above it

    

This is the equation of straight line with slope =3 and y intercept=0.5

At t =2 sec,

3) From t=2 sec to t=3sec,

You stood still in this time interval

∴

This is the equation of a line passing through the horizontal axis

  

This is the equation of line parallel to horizontal axis at a distance of 6.5 units from it.

At t =3 sec,

4) From t=3 sec to t=4sec,

Now, you move with velocity of towards the detector

∴

This is the equation of line parallel to horizontal axis at a distance of 4 units below it

This is the equation of straight line with slope = -4 and y intercept=18.5

At t =4 sec,

5) From t=4 sec to t=7sec,

You stood still in this time interval

∴

This is the equation of a line passing through the horizontal axis

This is the equation of line parallel to horizontal axis at a distance of 2.5 units from it.

Using these equations we can draw the graphs as given below.

a)

b)