Physics Help in: Motion Along A Straight Line- Example Problems with Solutions
Here are three practice problems, with increasing difficulty for you to try out. (But don't stop practicing with these three problems!) These are from Fundamentals of Physics, Halliday, 9E, with the corresponding numbers from Chapter Two. (1,7,70)
PROBLEMS ARE MOVING TO HERE: Motion Along A Straight Line Problems
1.During a hard sneeze, your eyes might shut for 0.5s. If you are driving a car at 90km/h during such a sneeze, how far does the car move during that time?
1 List your givens, and figure out/ understand what you're solving for. Look for the appropriate equations to use.
2 Notice that the velocities are NOT in standard units. Now is the time to convert them. Notice how the units cancel out diagonally. You can convert this all at once, and not in the two separate steps like I did.
3 Use your givens to plug into equations to solve. If one equation doesn't seem to work out, try another- shouldn't be a major issue on this problem.
You should get an answer of 13 meters, rounding to two significant figures, because that is how accurate your answer can be.
7. Two trains, each having a speed of 30km/h, are headed at each other on the same track. A bird that can fly 60 km/h flies off the front of one train when they were 60km apart and heads directly to the other train. On reaching the train, the bird flies back to the first train. What is the total distance the bird travels before the trains collide?
1 Draw a diagram and list your givens! The diagram will help you visualize the situations, because just reading this question can be overwhelming and discouraging. I didn't show my work for converting, for time's sake, but you probably should.
2 After reading this problem carefully, you should realize that you have two unknowns, and that you need to solve for time, t, first. So, you solve for the time the trains collide.
3 You can use the time that you solved for and sub it into the average velocity equation to find the displacement of the birdy.
You should get an answer of 60km. Also, you did not need to convert for this problem, fyi. But practice couldn't hurt. ;)
70. Two particles move along an x axis. The position of particla 1is given by x=6.00t2+3.00t+2.00 (in meters and seconds);the acceleration of particle 2 is given by a=-8.00t (in meters perseconds squared and seconds) and, at t=0, its velocity is 20m/s. When the velocities of the particles match, what is their velocity?
1 List your information about particle one and particle two.
2 Remember that the derivative of position is velocity. You are all set (for now) with particle one.
3 This is tricky. For particle two, you are given the acceleration. If you know that the derivative of velocity is acceleration, than you know that the integral of acceleration is velocity.
4 When you took the integral of acceleration (hopefully you remembered!), you added a constant of integration at the end. If you look back in the problem, you are given initial-value information to solve for the constant and therefore, get your velocity equation for particle 2.
5 Since the particles' velocities have to match, you have to set the two equations equal to each other, and then solve for zero. HINT: Notice how the equation can't be factored out.
6 Since you couldn't factor out, you probably knew to use to quadratic formula. I subbed in all the numbers and multiplied them out. Solving the quadratic formula gave us two times. One was rejected because you cannot have a negative time.
7 Don't forget what the question is asking for! You're not done just yet. You have to solve for the particles' velocity. I checked them both, to make sure I got the same numbers, letting me know I solved the problem correctly.
Your answer should be 15.6 m/s!
Hope this helped ya a little! Any problem suggestions from this chapter in Halliday's book, let me know!
Answers: 1. 13m; 7. 60km; 70. 15.6m/s
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