(Fist) QUESTION 1 [5 points] An object moves in 1 dimension It stats at est and unifomly acceleates at 5m/s fo s It then moves with constant velocity fo 4s It then unifomly acceleates at m/s until it comes to est a) What is total time of the jouney? [5 pts] Fom to s: v = 5t At t=s, v=1m/s Fom s to 6s: v = 1m/s Fom 6s to T: v = -(t-6)+1 At T, v= Thus T=11s b) What distance has the object taveled? [5 pts] Fom s to s: x=1/ 5t At s, x=1m Fom s to 6s: x = 1(t-)+1 At 6s, x=5m Fom 6s to 11s: x=-(t-6) +1(t-6) +5 At 11s, x=75m c) What is the aveage velocity duing the motion? [5 pts] v avg =Dx/Dt = 75/11= 68m/s d) What is the aveage acceleation duing the motion? [5 pts] v avg =Dv/Dt = /11= m/s e) Daw the gaph of the position vesus time x(t) and velocity vesus time v(t) fo the entie motion Include the values of x and v at t=s, t=6s and at the end of the motion [5 pts] x (m) v (m/s) 75 1 5 6 11 t (s) 1 6 11 t (s)
(Fist) QUESTION [5 points] Pats A, B, and C ae independent of one anothe A Conside two displacement vectos: A = ( 5cm) xˆ (cm) yˆ and B = ( 1cm) xˆ + (4cm) yˆ In the figue at ight assume that each gid squae epesents 1 cm x 1 cm i [pt] Stating fom the oigin, sketch and label A y ii [pt] Stating fom the oigin, sketch and label B iii [pt] Stating fom the oigin, sketch and label B iv [pts] Using the gaphical method, detemine and label A B B on the figue v [pts] Calculate the length of A A = (5 + (-) ) 5 =59cm vi [pts] Calculate the length of B B = ((-1) + 4 ) 5 =41cm B A x A B B Two displacement vectos, C and D, ae shown at ight i [pts] Sketch C + D in the diagam ii [5pts] Calculate C + D (hint: expess C and D in tems of the unit vectos î and ĵ ) C = 4ˆ i D = cosî + sin ĵ C + D = ( 4)ˆ i + ˆj C + D = ( 4) + 1 = 48m C C + D 4 m m D C t T 4π v a [5pts] Let the symbols " v ", " a ", and "t " denote a velocity, an acceleation, and a time, espectively Use dimensional analysis to show that the fomula v t = 4π cannot be physically valid Explain you answe a LT LT 1 = T T
(Fist) QUESTION [5 points] y At time t= a ball is thown with a speed of v at an angle of fom the hoizontal fom a height of h metes above the gound Let g> denote the absolute value of the gavitational acceleation due to the Eath Expess each of you answes blow in tems of v, h, g and You must show you wok and/o explain you answes to get full cedit Ignoe ai fiction Fo all pats that ask fo vecto answes, you must specify eithe the diection and magnitude o the components of the vecto h v a) [6 pts] What is the instantaneous velocity vecto when the ball is at the highest point of its tajectoy? The velocity is hoizontal (v y =dy/dt=), thus v = v iˆ = v cos iˆ x b) [ pts] What is the instantaneous acceleation vecto when the ball is the highest point of its tajectoy? a = gj ˆ c) [5 pts] At what time does the ball each the highest point of its tajectoy? 1 y = gt + sin( ) t + h dy sin At the top, =, i e ttop = dt g d) [8 pts] What is the displacement vecto when the ball is at the highest point of its tajectoy? At the highest point, sin 1 sin xtop = cos ttop =, and ytop = gt top + sin( ) ttop + h = At the stat point, x =, and y stat = h stat = top stat sin v sin iˆ = + ˆj e) [ pts] Which (if any) of you answes to pats (a) though (d) above would change if the initial height h wee doubled? h doesn't appea in any final answe No answe would change
(Fist) Pats A and B ae independent QUESTION 4 [5 points] Q A [9 pts] In an amusement pak ide, a spaceship stats fom est at point P and moves with inceasing speed along the path shown in the side view diagam at ight Daw aows to indicate the diection of the acceleation of the spaceship at points P, Q, and R (No explanation necessay) P R B Two spintes, A and B, tain togethe on a hoizontal staight tack The velocity vectos of the spintes ae shown fo instants 1-4, sepaated by equal time intevals, in the table below Fo the entie inteval fom instant 1 to instant 4, spinte A is ahead of spinte B (ie, spinte A is located to the left of spinte B) velocity vectos of spinte A velocity vectos of spinte B at instant 1 at instant at instant at instant 4 i [4 pts] In the boxes below, daw aows to epesent the diection of the aveage acceleation of each spinte fo the inteval fom instant 1 to instant 4 Aow showing the diection of the aveage acceleation of spinte A Aow showing the diection of the aveage acceleation of spinte B ii [4pts] Is the magnitude of the aveage acceleation of spinte A geate than, less than o equal to the magnitude of the aveage acceleation of spinte B? Explain you easoning Between the two instants 1 and 4: Dv A = units and Dv B =6units Since a avg =Dv/Dt, a < a A avg B avg (Question 4 continues on the next page)
(Fist) iii [4 pts] Fo a small time inteval stating at instant 1, does the distance between spinte A and spinte B incease, decease, o emain the same? Explain you easoning Duing that small inteval v A >v B The distance between A and B inceases iv [4 pts] Is the distance between spinte A and spinte B at instant geate than, less than, o equal to the distance between spinte A and spinte B at instant? Explain you easoning Between and, v A >v B The distance between A and B is geate at instant than at instant