asked by @jakee5 •
almost 2 years ago •
Physics
• 5 pts

Can you please explain the approach to finding average acceleration and velocity (the last two parts of the problem below).

**AVERAGE VELOCITY**

To find the average velocity, we can use the definition:

**v_av** = **Delta x**/Delta t

Note that I'm using bold to denote vectors. In this case, **Delta x** is the DISPLACEMENT, not the distance traveled. Moving from point A to point C, the displacement is 80 m (the diameter of the semicircular part of the track). The displacement is to the left of the figure, which is in the -x direction according to the coordinate system in the figure (it's hard to see the coordinates, but they're there). Noting that the **i** unit vector is in the +x direction, so the -**i** unit vector is in the -x direction, the displacement of the runner is

**Delta x** = -(80 m)**i**

Now, we're told it takes the runner 15 s to go from point A to point B and another 20 s to go from point B to point C, so

Delta t = 15 + 20 = 35 s

This means that the average velocity is

**v_av** = -(80 m)**i** / 35 s = -(2.29 m/s)**i**

**AVERAGE ACCELERATION**

The average acceleration is, by definition

**a_av** = **Delta v** / Delta t

where **Delta v** is the change in VELOCITY, not speed. At point A, the velocity is

**vA** = (8 m/s)**j**

or 8 m/s in the +y direction (up). At point B, the velocity is

**vB** = -(7 m/s)**i**

or 7 m/s in the -x direction (left). At point C, the velocity is

**vC** = -(6 m/s)**j**

or 6 m/s in the -y direction (down). So, we need to find both **Delta v** and Delta t from points A to B (which we'll call "trip 1"), and from points B to C (which we'll call "trip 2"). From A to B:

**Delta v1** = -(7 m/s)**i** - (8 m/s)**j**

Delta t1 = 15 s

From B to C:

**Delta v2** = -(6 m/s)**j** - [-(7 m/s)**i**] = (7 m/s)**i** - (6 m/s)**j**

Delta t2 = 20 s

So, the average accelerations are:

**a1** = [-(7 m/s)**i** - (8 m/s)**j**] / 15 s = -(0.47 m/s^2)**i** - (0.53 m/s^2)**j**

**a2** = [(7 m/s)**i** - (6 m/s)**j**] / 20 s = (0.35 m/s^2)**i** - (0.4 m/s^2)**j**

answered by @doug •
almost 2 years ago

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