PROBLEMSThe next two questions concern the graph shown below. This graph shows v, the one-dimensionalvelocity of a cart, as a function of time. The cart started its motion from rest at position x = 0.1) Which of the following statements about a2.5, the acceleration of the cart at time t =2.5 s?, is true?a2.5 < 0a2.5 = 0a2.5 > 02) Which of the following statements about x3, the position of the cart at time t = 3 s?,is true?x3 < 0x3 = 0x3 > 03) A car’s initial velocity is along the -x (negative x) direction. As it slows to a stop,its acceleration points in the +x direction.truefalseTwo boats, each capable of moving in still water at a constant velocity v = 6 m/s, setout to cross a river of width W = 20 m. Boat 1 heads directly across the river whileboat 2 is pointed at an angle q = 60 degrees with respect to the shore as shown in thediagram below. The current in the river moves at speed v0 = 2 m/s as shown. The nexttwo questions pertain to this situation.4) Which boat takes the least amount of time to cross the river?Boat 1 takes the least time.Boat 2 takes the least time.Each boat takes the same amount of time.5) Which boat moves with the greater speed with respect to the shore?Boat 1 moves with the greater speed with respect to the shore.Boat 2 moves with the greater speed with respect to the shore.Two projectiles are launched from a cliff of height H = 16m as shown in the diagrambelow. Projectile 1 is launched with velocity v1 = 12 m/s at an angle q1, where q1 = 35degrees. Projectile 2 is launched with velocity v2 = 12 m/s at an angle q2, where q2 =50 degrees. The next two questions pertain to this physical situation.6) If the projectiles are lauched at the same time, which projectile lands first?Projectile 1 lands first.Projectile 2 lands first.The projectiles land at the same time.Here we have two vectors V and W. The angle between these vectors is A.7) What is the component of V parallel to W in terms of A and the magnitudesof V and W?VWV sin(A)V cos(A)W sin(A)W cos(A)8) What is the component of V perpendicular to W in terms of A and the magnitudesof V and W?VWV sin(A)V cos(A)W sin(A)W cos(A)Now assume A=(3 m, 4 m) and B=(5 m, -3 m), where the first number is the xcomponent of the vector, and the second number is the y-component of the vector.9) What is the magnitude of vector A?7m4m(8 m, 1 m)5m(3 m, 4 m)10) What is A + B?(8 m, 1 m)7m(3 m, 1 m)10.83 m5.83 m(7 m, 2 m)A block of mass 5 kg is suspended by two ropes as shown in the picture below.The angle that the right rope makes with the horizontal is q= 45 degrees.11) If the mass of the block was increased the tension in the left rope wouldIncreaseDecreaseRemain the sameTwo blocks are being pushed across a horizontal floor with a coefficient of kineticfriction m=.3 . The mass of block A is 3kg, and the mass of block B is 2 kg.12) If the force being applied by the finger is F, what is the force that block A appliesto block B?FAonB = FFAonB = F/2FAonB = 2F/513) If the force applied by the finger was doubled, the acceleration of the blockswould be:less than twice as muchexactly twice as muchmore than twice as muchA cart with a mass of 20kg is initially at rest on a horizontal frictionless surface and isattached to a block of 5kg hanging vertically.14) If ONLY the mass of the cart was doubled, then the tension in the rope as theblock was falling would…remain the samedecreaseincreaseThe same constant force, F, is applied to two blocks. The first block has a mass of Mand the second block has a mass of 2M. Both blocks are initially at rest and the forceacts on each of them for the same period of time, t.15) After time, t, which block has more momentum?The block of mass MThe block of mass 2MThey will have the same momentum16) After time, t, which block has more kinetic energy?The block of mass MThe block of mass 2MThey will have the same kinetic energy17) After time, t, which block is moving the fastest?The block of mass MThe block of mass 2MThey will have the same speedA man with a mass of 100kg is standing on a uniform plank of mass 50kg. The man isstanding directly above the right support and the left support is located at the left endof the plank.18) If the man’s mass was doubled, but he stood in the same location, the force on theplank by the left support would:remain the samedecreaseincreaseA solid disk (I=1/2mr2)of mass 0.75kg is initially at rest at the top of an incline ofheight h=2m.19) If instead a solid sphere (I=2/5mr2)was allowed to roll down the same incline atthe bottom its velocity would bethe same as the solid diskless than the solid diskgreater than the solid diskIn Case 1 two people pull on the same end of a spring whose other end is attached to awall. In Case 2, the same two people pull with the same forces, but this time onopposite ends of the spring.20) In which case does the spring stretch the most?Case 1Case 2They will stretch the same amount21) If you want to send a signal using sound waves quickly, what material should yousend it through?airwaterleadouter space22) If your guitar is playing a note that is too low, (frequency is too low) you should:Loosen that stringTighten that stringThrow it awayJoin a rock band
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