Linear Motion Test Review 1. What is the slope o the graph o position versus time? LOOK IT UP IN YOUR NOTES 2. What is the slope o the graph o velocity versus time? LOOK IT UP IN YOUR NOTES 3. Name three ways to accelerate. LOOK IT UP ON YOUR 2.3 GUIDED READING 4. What does it mean when the sign o the acceleration is dierent than the sign o the velocity? Object is slowing down. 5. What does it mean when the sign o the acceleration is the same as the sign o the velocity? Object is speeding up. 6. What is the dierence in instantaneous and average acceleration? Look it up in your 2.3 guide reading. 7. What does the mathematical symbol lim represent? What does this mean? Lim stands or limit. It means the value o an expression as some part o it approaches a certain value. 8. What is the acceleration due to gravity? LOOK IT UP IN YOUR NOTES 9. An object is thrown in the air. Describe the object s velocity and acceleration on the way up, at the top, and on the way down? LOOK AT YOUR FREE FALL PATTERNS EXERCISE 10. Which kinematic equation requires you to use the quadratic ormula to solve or time? 3rd 11. What are the underlying assumptions o the kinematics equations? Linear motion & constant acceleration. 12. How does the velocity o an object thrown straight up compare to the velocity at the same elevation on its way back down? LOOK AT YOUR FREE FALL PATTERNS EXERCISE 13. How does the speed o an object thrown straight up compare to the speed at the same elevation on its way back down? LOOK AT YOUR FREE FALL PATTERNS EXERCISE 14. What do each o the three numbers mean that are computed in a linear regression analysis? Slope, y-intercept, correlation coeicient
15. In a drag race, a dragster reaches the quarter mile (402 m maker with a speed o 80 m/s. What is his acceleration and how long did the run take. 402m,x i 0, 80m /s, 0 2 2 + 2a( a v 2 2 2( v 2 2 t a (80m /s2 2( 402m 80m /s 7.96m /s 2 10.05s 7.96m /s2 16. A body is released rom rest and alls reely. Compute its position and velocity ater 1,2,3, and 4 seconds. Take the origin 0 at the elevation o the starting point, and the upward direction as positive. +at 0+ ( 9.8m /s 2 t ( 9.8m /s 2 t x i + t+ 1 2 at2 0+ 0+.5( 9.8m /s 2 t 2 ( 4.9m /s 2 t 2 t(sec v(m/s x(m 0 0 0 1-9.8-4.9 2-19.6-19.6 3-29.4-44.1 4-39.2-78.4 17. A ball is thrown upward with an initial speed o 80 t./sec. How high does it go? What is its speed at the end o 3.0 seconds?
c How high is it at that time? 80t /s,a 32t /s 2 2 2 + 2a( 2 2a v 2 i 2a (80t /s 2 2( 32t /s 2 100t. +at 80t /s (32t /s 2 (3s 16t /s c x i + t+ 1 2 at2 (80t /s(3s 1 2 (32t /s2 (3s 2 96t 18. Find an equation or the best line through the points below using linear regression. x y 1 3.05 2 5.1 3 6.98 4 8.99 5 12.0 y(2.179x+0.687 You must know how to do this on a TI-83 or TI-84. 19. Find an equation or the best line through the points below using linear regression x y 2 7.85 4 13.5 6 20.0 8 25.95 10 31.75 y(3.0125x+1.735 You must know how to do this on a TI-83 or TI-84.
20. A speed boat increases its speed rom 50 t/s to 80 t/s in a distance o 200 t. Find the magnitude o its acceleration and the time it takes the boat to travel this distance. 200t,x i 0, 80t /s, 50t /s 2 2 + 2a( a v 2 2 (80t /s2 (50t /s 2 2 2 200t t a ( 80t /s 50t /s 9.75t /s 2 3.08s 9.75t /s 2 21. The acceleration o gravity on the moon is about one sixth as great as on the earth. A stone is thrown vertically upward on the moon, with an initial speed o 20 m/s. How long will the stone remain in motion? What is the maximum height reached by the stone relative to the moon's surace? 20m /s, v top 0 a 1 6 ( 9.8m /s2 1.63m /s 2 t up 0 20m /s 12.3s a 1.63m /s 2 t total 2xt up 2 *12.3s24.6s x i + t+ 1 2 at2 (20m /s(12.3s+ 1 ( 1.63m /s212.3s 2 ( 2 123m 22. A proton has an initial velocity o 2.5 x10 5 m/s and undergoes a uniorm deceleration o 5.0 x 10 10 m/s 2. What is its velocity ater moving through a distance o 10 cm? 2.5x10 5 m /s,a 5x10 10 m /s 2, 10cm,x i 0 2 2 + 2a( (2.5x10 5 m /s 2 + 2( 5x10 10 m /s 2 (0.1m 2.3x10 5 m /s
23. A bullet is ired through a board, 10 cm thick, in such a way that the bullet's line o motion is perpendicular to the ace o the board. I the initial speed o the bullet is 400 m/s and it emerges rom the other side o the board with a speed o 300 m/s, ind the deceleration o the bullet as it passes through the board and the total time the bullet is in contact with the board. 400m /s, 300m /s, 0.1m,x i 0 2 2 + 2a( a v 2 2 2 t a ( 300m /s 2 400m /s 2(0.1m ( 2 ( 300m /s 400m /s 350,000m /s 2 ( 350,000m /s 2 2.86x10 4 s 24. A go cart travels the irst hal o a 100 m track with a constant speed o 5 m/s. In the second hal o the track, it experiences a mechanical problem and decelerates at 0.2 m/s 2. How long does it take the go-cart to travel the 100 m distance. 1 x 50m,v 5m / s,a 0 t x v 50m 5m /s 10s 2 5m /s, x 50m,a 0.2m /s 2 x i + t + 1 2 at 2 50m (5m /st +.5( 0.2m / s 2 t 2 Use quadratic equation to solve. t 13.82sec (ignore second time, its another lap t total 10s + 14s 24s 25. The position time graph o a particle moving along the x axis is shown below. Determine whether the velocity is positive, negative, or zero or the times t 1, t 2, t 3, and t 4. t 1 >0 t 2 0 t 3 <0 t 4 0
26. The velocity time graph or an object moving along the x axis is shown below. Plot a graph o the acceleration versus time. v(m/s a(m/s 2 t(s t(s 27. Based on the ollowing inormation, determine i the object is speeding up, slowing down, moving to the right or moving to the let. Velocity Sign Acceleration Sign Direction Speeding Up or Slowing Down + - + + - - - + To complete this question, reer to your answer to numbers 1-2 & 4-5.