Kinematics in 1D Question

We are multiplying both sides by 1/0.447 in order to get rid of the fraction in the denominator on the LHS. This is a common algebraic method used to solve equations.
  • #1
crono_
44
0

Homework Statement



Problem taken from Cutnell & Johnson 8th Edition Textbook (though it's also in the 7th edition as well, can't recall question # though). It is from chapter 2, question # 10.

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?

Known Data:

vavg = 1.34 m/s, due west. For whole trip.

1st Stretch

x1 = 6.44 km = 6440 m

vavg = 2.68 m/s, due west

t1 = 6440 m / 2.68 m/s = 2402 s

2nd Stretch

x2 = ?

vavg = 0.447 m/s, due east

t2 = ?

I took the left direction as positive and the right negative.

Homework Equations



vavg = [tex]\Delta[/tex]x / [tex]\Delta[/tex]t

The Attempt at a Solution



This is where I get lost. I looked up some online solutions but was unable to follow them. One of them started:

vavg = 1.34 m/s = x1 - x2 / t1 - t2

1.34 m/s = 6440 - x2 / 2403 s + (x2 / 0.447 m/s)

The next step was to solve for x2 but I'm stuck here as x2 is in the equation twice. How do you solve for something that's in two parts of the equation? Factoring didn't seem to work, granted I may have done it incorrectly.

I hope this makes sense, it's a lot of work to type up everything in these forums. But the help is usually worth it. Any assistance would be greatly appreciated.

Thanks in advance!
 
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  • #2
1.34 m/s[2403 s + 2.237*x2s] = 6440 - x2.
1/0.447 = 2.237
Now remove the bracket in LHS and collect the terms of x2 from both sides and solve for x2.
 
  • #3
Ok...

Why are we 1/0.447? Where does the 1 come from?
 
  • #4
x2/O.447 = x2*(1/0.447)
 

1. What is kinematics in 1D?

Kinematics in 1D is a branch of physics that studies the motion of objects in one dimension, such as along a straight line. It involves analyzing the position, velocity, and acceleration of an object over time.

2. What is the difference between displacement and distance?

Displacement refers to the change in position of an object from its initial position to its final position, while distance refers to the total length of the path traveled by the object. Displacement is a vector quantity, while distance is a scalar quantity.

3. What is the difference between speed and velocity?

Speed refers to how fast an object is moving, while velocity refers to the speed and direction of an object's motion. Speed is a scalar quantity, while velocity is a vector quantity.

4. How do you calculate acceleration in 1D?

Acceleration in 1D can be calculated by dividing the change in velocity by the change in time. The formula for average acceleration is a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval.

5. How do you use kinematics equations to solve problems?

To use kinematics equations to solve problems, you first need to determine which variables are known and which are unknown. Then, you can choose the appropriate equation that relates those variables and solve for the unknown. It is important to pay attention to units and use consistent units throughout the calculation.

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