# Two Equations for Average Velocity?

• Spooky123
Spooky123
Homework Statement
You walk in the direction of the unit vector <1,0, 0> a distance of214 m at a constant speed of 3.6 m/s, then turn and walk in the direction of the unit vector <1, 0, 1>/ root 2 for a distance of 16 m at a constant speed of 3 m/s. What was your average velocity?
Relevant Equations
Vavg = delta r / delta t
I know that average velocity is the change in position over the change in time. But im getting conflicting views from other sources saying thats its the total distance divided by the total time. For this question we would first find the respective vectors by multiplying the distance with the given unit vectors. Then according to the average velocity formula we would find the difference between both vectors (change in position). To find the respective times, we would use the distance divided by the speed given for each. Using the final formula for avg velocity should give us the answer.

R1 = <21,0,0>m
R2 = <11.31,0,11.31>m
Delta R = R2 - R1
= <-9.69,0,11.31>

t1 = d1/v1 = 21/3.6 = 5.833
t2 = d2/v2 = 16/3 = 5.33
Delta t = t2 - t1 = -0.5

Thus, Average velocity = Delta R / Delta T?

Is this the right way to go about it?

Hi @Spooky123. Welcome to PF.

Spooky123 said:
I know that average velocity is the change in position over the change in time.
Ok but it might be clearer to say that average velocity is the total displacement divided by the total time taken.

Spooky123 said:
But im getting conflicting views from other sources saying thats its the total distance divided by the total time.
Average velocity is a vector. The total distance covered (a scalar) divided by the total time taken (also a scalar) gives the average speed, not the average velocity.

Spooky123 said:
For this question we would first find the respective vectors by multiplying the distance with the given unit vectors. Then according to the average velocity formula we would find the difference between both vectors (change in position). To find the respective times, we would use the distance divided by the speed given for each. Using the final formula for avg velocity should give us the answer.

R1 = <21,0,0>m
R2 = <11.31,0,11.31>m
Delta R = R2 - R1
= <-9.69,0,11.31>
No. <21, 0, 0>m is not a position vector, It's a displacement (change in position). Similarly for <11.31, 0 , 11.31>m.

To get the total displacment you must add the individual displacements. E.g. if you move 5m in the +x-direction and then 10m in the +x-direction, your total displacement is 15m in the x direction.

Spooky123 said:
t1 = d1/v1 = 21/3.6 = 5.833
t2 = d2/v2 = 16/3 = 5.33
Delta t = t2 - t1 = -0.5
No. If the first part of the journey takes time t₁ and the second part takes time t₂, the total time for the whole journey is ???

Spooky123 said:
Thus, Average velocity = Delta R / Delta T?

Is this the right way to go about it?
If ΔR were the correctly calculated total displacement and ΔT were the correctly calculated total time, that formula would be correct.

MatinSAR and Spooky123
Average velocity = Change in position vector divided by time interval.
Average speed = Total distance traveled (odometer reading from start to finish) divided by time needed to travel that distance.

Two different ideas. If it takes you time ##T## to go around a complete circle of radius ##R##, then
Average velocity = Zero.
Average speed = ##\dfrac{2\pi R}{T}.##

Your approach for finding the average velocity is correct. Note that for motion at constant velocity in a straight line, the average velocity has magnitude equal to the average speed. You rely on this idea to find the correct times required to travel in each direction separately and then add the times to find the total time over which the displacement takes place. Note that when an object moves at constant speed along a curved line, the average speed and the average velocity have different magnitudes.

MatinSAR

## What is the first equation for average velocity?

The first equation for average velocity is $$v_{avg} = \frac{\Delta x}{\Delta t}$$, where $$\Delta x$$ is the change in position (displacement) and $$\Delta t$$ is the change in time.

## What is the second equation for average velocity?

The second equation for average velocity, used when acceleration is constant, is $$v_{avg} = \frac{v_i + v_f}{2}$$, where $$v_i$$ is the initial velocity and $$v_f$$ is the final velocity.

## When should I use the first equation for average velocity?

You should use the first equation for average velocity ($$v_{avg} = \frac{\Delta x}{\Delta t}$$) when you know the total displacement and the total time taken for that displacement.

## When should I use the second equation for average velocity?

You should use the second equation for average velocity ($$v_{avg} = \frac{v_i + v_f}{2}$$) when you have constant acceleration and you know the initial and final velocities.

## Can the two equations for average velocity be used interchangeably?

No, the two equations for average velocity cannot be used interchangeably. The first equation applies to any situation where you know the total displacement and time, while the second equation specifically applies to situations with constant acceleration and known initial and final velocities.

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