Lesson 1.6: Calculating Displacement During Accelerated Motion
Completion requirements
Lesson 1.6: Calculating Displacement During Accelerated Motion
A vehicle must pick up speed in the acceleration lane before merging into highway traffic. When designing an acceleration lane, you have to decide how long to make it. This decision requires you to calculate how far a vehicle will travel while catching up to the speed of highway traffic.
In this lesson, two equations are developed for solving problems involving uniform accelerated motion. Your challenge will be choosing the equation that helps you solve the problem. This is the aspect of problem solving that you are
trying to improve. By the end of the chapter there will be several expressions for calculating displacement. You will need to first identify the motion and uniform velocity or uniform acceleration, then apply a suitable equation.
For an object moving with uniform motion, you can simply determine its displacement by using the formula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«mi»d«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»V«/mi»«mi»§#916;«/mi»«mi»t«/mi»«/math» .
Two new equations are developed that apply to accelerated motion. You will see how the new equations are developed graphically. Students often find this challenging, but you will not be evaluated on this. Instead the focus of evaluation will be on applying the equations to solve motion problems.
- Read pages 205 - 206
First Displacement Equation
You may read pages 207 or view the video on the right.
Note That deriving this equation comes from the idea that the area under a velocity-time graph gives the displacement.
- Work through Examples 1.15 and 1.16 on pages 208 and 209 of your textbook. View these two examples if you need more examples. Do
Practice Problems 32 and 33 and check your answers in the “Practice Answers”
Second Displacement Equation
You may read page 210 or view the video on the right.
What is the basic idea used to derive this equation?
What is the basic idea used to derive this equation?
- Work through the Example problems on the textbook. Do Practice Problems 34 and 35. Check your answers with those in the “
Practice Answers”. View this video
if you would like to see another example. [Note: ignore the end when he solves for time - you will not need to do this]
Check your answers with those in the “Practice Answers” in the online course.
When merging into traffic from an acceleration lane, a vehicle might accelerate at a rate as high as 3.0 m/s2. In When merging into traffic from an acceleration lane, a vehicle might accelerate at a rate as high as 3.0 m/s2. In contrast, the magnitude of the acceleration of a falling object—say a pen off the edge of a desk—is a constant 9.81 m/s2. This acceleration downward is due to gravity.
- Read “Acceleration Due to Gravity” on page 208 and “1.6 Summary” on page 212.
- Read “1.6 Summary” on page 212 of the textbook and complete questions 3 and 4. Check your answers with those in the “Practice Answers” in the online course. It is recommended you do the self check question below.
In the end, choosing the correct formula is the one of the biggest barriers students have in problem solving. View the video on the right to see how the best equation is chosen
A person at the edge of a tall building throws a ball vertically upward with a velocity of 3 m/s. What isll be the displacement of the ball 0.5 s and 5.0 s after the ball is thrown.
Check you answer using the video on the right. It has many problem solving tips as well.
A person at the edge of a tall building throws a ball vertically upward with a velocity of 3 m/s. What isll be the displacement of the ball 0.5 s and 5.0 s after the ball is thrown.
Check you answer using the video on the right. It has many problem solving tips as well.