Linear Motion Test Review 1. What is the slope of the graph of position versus time? LOOK IT UP IN YOUR NOTES 2. What is the slope of the graph of 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 of the acceleration is different than the sign of the velocity? Object is slowing down. 5. What does it mean when the sign of the acceleration is the same as the sign of the velocity? Object is speeding up. 6. What is the difference 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 for limit. It means the value of an expression as some part of 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 formula to solve for time? 3rd 11. What are the underlying assumptions of the kinematics equations? Linear motion & constant acceleration. 12. How does the velocity of 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 of 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 of the three numbers mean that are computed in a linear regression analysis? Slope, y-intercept, correlation coefficient 15. In a drag race, a dragster reaches the quarter mile (402 m) maker with a speed of 80 m/s. What is his acceleration and how long did the run take. x f = 402m,x i = 0,v f = 80m / s,vi = 0 v 2f = v2i + 2a(x f − x i ) a= v 2f − vi2 v2 (80m / s)2 = f = = 7.96m / s 2 2(x f − x i ) 2x f 2(402m) t= v f − vi 80m / s = = 10.05s 2 a 7.96m / s 16. A body is released from rest and falls freely. Compute its position and velocity after 1,2,3, and 4 seconds. Take the origin 0 at the elevation of the starting point, and the upward direction as positive. v f = vi + at = 0 + (−9.8m / s 2 )t v f = (−9.8m / s2 )t 1 2 2 2 at = 0 + 0 + .5(−9.8m / s )t 2 x f = (−4.9m / s 2 )t 2 x f = x i + vi t + t(sec) 0 1 2 3 4 vf(m/s) 0 -9.8 -19.6 -29.4 -39.2 xf(m) 0 -4.9 -19.6 -44.1 -78.4 17. A ball is thrown upward with an initial speed of 80 ft./sec. a) How high does it go? b) What is its speed at the end of 3.0 seconds? c) How high is it at that time? 2 vi = 80 ft / s,a = −32 ft / s a) v 2f = v2i + 2a(x f − x i ) vi2 = −2ax f xf = −vi2 −(80 ft / s) 2 = 2 = 100 ft. 2a 2(−32 ft / s ) b) 2 v f = vi + at = 80 ft / s − (32 ft / s )(3s) = −16 ft / s c) x f = x i + vi t + 1 2 1 at = (80 ft / s)(3s) − (32 ft / s2 )(3s)2 = 96 ft 2 2 18. Find an equation for 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=(2.179)x+0.687 You must know how to do this on a TI-83 or TI-84. 19. Find an equation for the best line through the points below using linear regression y x 2 7.85 4 13.5 6 20.0 8 25.95 10 31.75 y=(3.0125)x+1.735 You must know how to do this on a TI-83 or TI-84. 20. A speed boat increases its speed from 50 ft/s to 80 ft/s in a distance of 200 ft. Find the magnitude of its acceleration and the time it takes the boat to travel this distance. x f = 200 ft,x i = 0,v f = 80 ft / s,vi = 50 ft / s a) v 2f = v2i + 2a(x f − x i ) a= v 2f − vi2 2x f 2 2 = (80 ft / s) − (50 ft / s) = 9.75 ft / s 2 2(200 ft ) = 80 ft / s − 50 ft / s = 3.08s 9.75 ft / s 2 b) t= v f − vi a 21. The acceleration of 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 of 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 surface? vi = 20m / s,v f = vtop = 0 a= 1 (−9.8m / s 2 ) = −1.63m / s 2 6 a) v f − vi 0 − 20m / s = = 12.3s a −1.63m / s2 = 2xtup = 2 *12.3s = 24.6s tup = ttotal b) x f = x i + vi t + 1 2 1 at = (20m / s)(12.3s) + (−1.63m / s 2 )(12.3s )2 = 123m 2 2 22. A proton has an initial velocity of 2.5 x105 m/s and undergoes a uniform deceleration of 5.0 x 1010 m/s2. What is its velocity after moving through a distance of 10 cm? vi = 2.5x105 m / s, a = −5x1010 m / s 2 , x f = 10cm, xi = 0 v 2f = v2i + 2a(x f − x i ) = (2.5x10 5 m / s) 2 + 2(−5x1010 m / s 2 )(0.1m) v f = 2.3x105 m / s 23. A bullet is fired through a board, 10 cm thick, in such a way that the bullet's line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 400 m/s and it emerges from the other side of the board with a speed of 300 m/s, find the deceleration of the bullet as it passes through the board and the total time the bullet is in contact with the board. vi = 400m / s,v f = 300m / s, x f = 0.1m, xi = 0 a) 2 2 v f = vi + 2a(x f − x i ) 2 2 v f − vi a= 2x f = (300m / s)2 − (400m / s)2 = −350,000m / s2 2(0.1m) b) t= v f − vi a = (300m / s) − (400m / s) −350,000m / s 2 = 2.86x10 −4 s 24. A go cart travels the first half of a 100 m track with a constant speed of 5 m/s. In the second half of the track, it experiences a mechanical problem and decelerates at 0.2 m/s2. How long does it take the go-cart to travel the 100 m distance. 1)∆x = 50 m , v = 5m / s, a = 0 ∆x 50 m t= = = 10 s v 5m / s 2) v i = 5m / s, ∆ x = 50 m , a = − 0.2m / s 2 1 2 at 2 50 m = (5m / s )t + .5( −0.2 m / s 2 )t 2 Use quadratic equation to solve. x f = x i + vi t + t = 13.82sec (ignore second time, t total = 10 s + 14 s = 24 s its another lap) 25. The position time graph of a particle moving along the x axis is shown below. Determine whether the velocity is positive, negative, or zero for the times t1, t2, t3, and t4. t1>0 t2=0 t3<0 t4=0 26. The velocity time graph for an object moving along the x axis is shown below. Plot a graph of the acceleration versus time. v(m/s) a(m/s2) t(s) t(s) 27. Based on the following information, determine if the object is speeding up, slowing down, moving to the right or moving to the left. Velocity Sign Acceleration Sign + + - + + Direction Speeding Up or Slowing Down To complete this question, refer to your answer to numbers 1-2 & 4-5.