For a fifth set of maneuvers, the astronaut’s partner calculated her average acceleration over the 2 s intervals to be -0.5m/s^2. If the initial velocity of the astronaut was -0.4m/s, what was her final? Did she speed up or slow down over the 2 s interval? Answer -1.4m/s, speed up The background info for the practice problem is in both photos. 36CHAPTER 2 Motion Along a Straight LineSOLUTIONSOLVE To find the astronaut's average acceleration in each case, we usethe definition of average acceleration (Equation 2.3): dav,x= Aux/At.SET UP We use the diagram in Figure 2.11 to organize our data.of The time interval is At = 2.0 s in all cases; the change in velocity indrientongeach case is Aux = U2xU1xPart (a): aav, xPart (a)Part (b)Part (c)Part (d)BEFOREx = 0.8 m/sUx= 1.6 m/sx = -0.4 m/sU1x = -1.6 m/sHxAFTERU2x = 1.2 m/sU2x = 1.2 m/sU2x = -1.0 m/s 1-V2x = -0.8 m/sA FIGURE 2.11 We can use a sketch and table to organize theinformation given in the problem.Part (b): dav, xPart (c): dav, xPart (d): dav, x =0.8 m/s2 s1.2 m/s4s1.2 m/s4s-1.0 m/s (-0.4 m/s)4s2s1.6 m/s2 s= +0.2 m/s²;= -0.2 m/s²;-0.8 m/s (-1.6 m/s)4s 2 sdecoq ai I.-0.3 m/s²;= +0.4 m/s².REFLECT The astronaut speeds up in cases (a) and (c) and slows downin (b) and (d), but the average acceleration is positive in (a) and (d) andnegative in (b) and (c). So negative acceleration does not necessarilyindicate a slowing down.Practice Problem: For a fifth set of maneuvers, the astronaut's partnercalculates her average acceleration over the 2 s interval to be -0.5 m/s².If the initial velocity of the astronaut was -0.4 m/s, what was her finalvelocity? Did she speed up or slow down over the 2 s interval? Answers:-1.4 m/s, speed up.Example 2.3 raises the question of what the sign of acceleration means and how itrelates to the signs of displacement and velocity. Because average acceleration (i.e., thex component) is defined as aav, x Av/At, and At is always positive, the sign of accelera-tion is the same as the sign of Av. Figure 2.12 shows the four possibleyou unders= Definition of average accelerationThe average acceleration day of an object as it moves from x₁ (at time ₁) to x₂ (attime 12) is a vector quantity whose x component is the ratio of the change in the x com-ponent of velocity, Aux = U2x U₁x, to the time interval, At = 1₂ - 1₁:Units: m/s²Notes:●dav, x =U2x U1x1₂ - 11AUXAtAverage acceleration is a vector.• It describes how the velocity is changing with time.(2.3)• The sign of the average acceleration is not necessarily the same as the sign of thevelocity. Furthermore, if the object is slowing down, then it does not necessarilyfollow that the acceleration is negative. Similarly, if the object is speeding up, it doesnot necessarily follow that it has positive acceleration.(a) U1x = 0.8 m/s,U2x = 1.2 m/s (speeding up);1.2 m/s (slowing down);U2x =(b) Ulx= 1.6 m/s,(c) U₁x = -0.4 m/s,U2x = -1.0 m/s (speeding up);(d) U₁x = -1.6m/s,U2x = -0.8 m/s (slowing down).If t₁ = 2 s and t₂ = 4s in each case, find the average acceleration for each set of data.▲ ApplicationHaven't I been here before?Although a Formula 1 race car travels atclose to 200 mph, for each lap of the racethe average velocity of the car is zero! Thisis because, from start to finish, the totaldisplacement of the race car is zero.EXAMPLE 2.3 Acceleration in a space walkIn this example we will use Equation 2.3 to calculate the acceleration of an astronaut on a space walk. Theastronaut has left the space shuttle on a tether to test a new personal maneuvering device. She moves alonga straight line directly away from the shuttle. Her onboard partner measures her velocity before and aftercertain maneuvers, and obtains these results:KAA1980Video Tutor DemoVideo Tutor SoluticCONTINUED

Given data: Time interval (Δt) = 2 s Initial velocity (v1x) = -0.4 m/s Acceleration (ax) = -0.5 m/s2 Required: The final velocity (v2x), speed up or slow down Using equation of motion v2x = v1x + ax∆t= (-0.4 m/s) + (-0.5 m/s2)(2 s)= -1.4 m/s The final velocity is equals to -1.4 m/s The speed is the magnitude of the velocity. Initially speed is equals to 0.5 m/s and final speed is 1.4 m/s So the speed of the astronaut is increased. Answer: Speed up