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versus I, and a. versus I, for the time interval I = 0 to , = 40 s. 2.16. An astronaut has left the Intemational Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a lO-s interval. What are the magni-tude, the algebraic sign, and the direction of the average accelera-tion in each interval? Assume that the positive direction is to the right. (a) At the beginning of the interval the astronaut is moving toward the right along the x-axis at 15.0 m/s, and at the end of the interval she is moving toward the rig" at 5.0 m/s. (b) At the begin-ning sbe is moving toward the left at 5.0 mIs, and at the end sbe is moving toward the left at 15.0 m/s. (c) At the beginning she is moving toward the right at 15.0 mIs, and at the end she is moving toward the left at 15.0 m/ •. 2.17. Auto Acceleration. Based on your experiences of riding in automobiles, estimate the magnitude of a car's average accelera-tion when it (a) accelemtes onto a freeway from rest to 65 milh, and (b) brakes from highway speeds to a sudden stop. (c) Explain why the average acceleration in each case could be regarded as either positive or negative. 118. A car's velocity as a function of time is given by vA,} = a + Pl2, wbere a = 3.00 m/s and p = 0.100 m/s'. (a) Calculate the average acceleration for the time interval, = 0 to , = 5.00 s.
64 CHAPTER 2 Motion Along a Straight line (b) Calculate the instantaneous acceleration for t = 0 and t = 5.00 s. (c) Draw accurate v.-t and a.-t graphs for the car's motion between t = 0 and t = 5.00 s. 2.19. Figure 2.35 is a graph of the coordinate of a spider crawling along the x-axis. (a) Graph its velocity and acceleration as func-tions of time. (b) In a motion diagram (like Fig. 2.13b and 2.14b), show the position, velocity, and acceleration of the spider at the flvetimest= 2.5s,t= IOs,t= 2Os,t= 30s,andt= 37.5s. Figure 2.35 Exercise 2.19. x{m) Parabola 2.28. The position of the front bumper of a test car under micro-processor control is given by x(t) = 2.17m + (4.80m/S2)t2-(0.100 m/S6)t6• (a) Find its position and acceleration at the instants when the car has zero velocity. (b) Draw x-t, v.-t, and a.-t graphs for the motion of the bwnper between t = 0 and t = 2.00 s. Section 2.4 Motion with Constant Acceleration 2.21. An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 7.00 s. Its speed as it passes the second point is 15.0 m/s. (a) What is its speed at the first point? (b) What is its acceleration? 2.n. The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A-18 Homet jet fighter from rest to a takeoff speed of 173 mi/h in a distance of 307 ft. Assume constant acceler-ation. (a) Calculate the acceleration of the fighter in m/s2. (b) Cal-culate the time required for the fighter to accelerate to takeoff speed. 2.23. A Fast Pitch. The fastest measured pitched baseball left the pitcher's hand at a speed of 45.0 m/s. If the pitcher was in contact with the ball over a distance of 1.50 m and produced con-stant acceleration, (a) what acceleration did he give the ball, and (b) how much time did it take him to pitch it?