Basic Kinematics Problem -- Backpacker's average velocity and distance....

In summary: So the total change in time is t1 + t2.Similarly, in the displacement equation, x2 represents the final displacement, not the change in displacement.In summary, the backpacker hiked for a total of 6.44 km, with an average velocity of 2.68 m/s, due west, and then turned around and hiked for an unknown distance with an average velocity of 0.447 m/s, due east. The total change in time was 2403 seconds. The equation for average velocity is Vavg = (xw + xe)/(tw + te), where xw is the west displacement, xe is the east displacement, tw is the time spent hiking west, and te is the time spent
  • #1
physlexic
14
0

Homework Statement


Problem reads:
In reaching her destination, a backpacker walks with an average velocity of 1.34 m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of 2.68 m/s, due west, turns around, and hikes with an average velocity of 0.447 m/s, due east. How far east did she walk?

Homework Equations


Vavg = delta X/ delta t

The Attempt at a Solution


I let
vw= average velocity from hiking west
xw = west displacement
tw = the time it took to travel in the west direction

ve = average velocity from hiking east
xe = east displacement
te = the time it took to travel in the east directionvw = 2.68 m/s
xw = 6.44 km = 6440 m
tw = 6440 m / 2.68 m/s = 2403 s

ve = 0.447 m/s
xe = ?
te = ?

using the avg. velocity equation as ve = xe / te I solve for xe where ve = 0.447 m/s
xe = te * 0.447 m/stherefore according to the equation Vavg = xe-xw / te-tw
However, I'm looking at other solutions and it shows the equation to be Vavg = xw + xe / te + te
I thought average velocity is a change in displacement over a change in time? So why are they adding the displacement & time as opposed to subtracting? So confused...
 
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  • #2
physlexic said:
I thought average velocity is a change in displacement over a change in time? So why are they adding the time as opposed to subtracting?
Because the total change in time is the sum of the two times and not the difference as the times are defined:
physlexic said:
t1 = the time it took to travel in the west direction
physlexic said:
t2 = the time it took to travel in the east direction
 
  • #3
But every Average Velocity equation is x2-x1 / t2-t1
at least that's what my book defines it...the change in time is the final time minus the initial time.

Same applies for displacement but yet they are adding it here as well.
 
  • #4
You need to look beyond symbols and realize what they are representing rather than simply try to apply a formula.

In this equation:
physlexic said:
But every Average Velocity equation is x2-x1 / t2-t1
t1 and t2 are the initial and final times, respectively.

In the equation in your OP, the times given are not the start and end times, it is the travel times.
 

Related to Basic Kinematics Problem -- Backpacker's average velocity and distance....

1. How is average velocity calculated in a basic kinematics problem?

In a basic kinematics problem, average velocity is calculated by dividing the total displacement (change in position) by the total time taken. This gives the average speed at which an object is moving over a certain distance.

2. What is the difference between velocity and speed in a basic kinematics problem?

In a basic kinematics problem, velocity is a vector quantity that takes into account an object's speed and direction of motion, while speed is a scalar quantity that only measures how fast an object is moving without considering direction.

3. How can distance be calculated using velocity and time in a basic kinematics problem?

Distance can be calculated by multiplying an object's average velocity by the total time taken. This gives the total distance traveled by the object over a certain period of time.

4. What is the equation for calculating displacement in a basic kinematics problem?

The equation for calculating displacement in a basic kinematics problem is Δx = xf - x0, where Δx represents the change in position, xf is the final position, and x0 is the initial position.

5. How does acceleration factor into a basic kinematics problem?

Acceleration is the rate of change of an object's velocity over time. In a basic kinematics problem, acceleration can be used to calculate the change in an object's velocity, which then affects the object's displacement and distance traveled.

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