1. (7 marks)An animal runs along a straight line. It starts from rest, accelerating at 2.00 m/s2until it reaches a speed of 12.0 m/s. Then, the animal starts to slow down in auniform manner (constant deceleration) for an additional 4.00 s until it stops.a. Determine the total distance traveled and the average velocity of the animal.b. Sketch the position – time graph for the motion of the animal. Assume that theanimal starts at x = 0.First part of the motion:?1 = ?10 + ?1?112.0 = 0 + 2.00??1 = 6.00 ?∆?1 = ?10?1 +1 2?1?12∆?1 = (0)(6.00) +1 2(2.00)(6.00)2 = 36.0 ?Second part of the motion:?2 = ?20 + ?2?20 = 12.0 + ?2(4.00)?2 = -3.00 ?∆?2 = ?20?2 +1 2?2?22 = (12.0)(4.00) + 12(-3.00)(4.00)2 = 24.0 ?Average velocity:???? =∆?1 + ∆?2?1 + ?2=36.0 + 24.06.00 + 4.00 = 6.00 ?/?2. (6 marks)A grasshopper launches itself at an angle of ? = 520 above the horizontal, asshown below. It lands on the grass a distance d = 4.0 m from the launching pointafter 0.90 s.a. Determine the magnitude of the initial velocity of the grasshopper.b. Determine the maximum height reached by the grasshopper.c. What is the velocity of the grasshopper when it reaches maximum height?d. What is grasshopper’s acceleration at the maximum height?Δx = ?0???0? = ?0???5204.0 = ?0(???520)(0.90)?0 = 7.2 ?/?? = ∆? = ?0? (2?) + 1 2 ?? (2?)2?0? = (7.2 ?/?)???520 = 5.67 ?/?? = (5.67 ?/? ) (0.290) + 1 2 (-9.8) (0.290)2 = 1.6 ?At the maximum height, the grasshopper has only the horizontal velocity equal to?0? = ?0(???520) = (7.2 ??)(???520) = 4.4 ?/?Acceleration is 9.8 m/s2 (downward)3. (8 marks)Three masses (m1 = 2.0 kg, m2 = 4.0 kg and m3 = 6.0 kg) are connected by twostrings of negligible mass, as shown below. The angle of inclination θ = 35.00. Thecoefficient of kinetic friction between the surfaces and masses m1 and m2 is 0.25.The pulleys are frictionless.a. Draw a free-body force diagram for each mass.b. Determine the force of kinetic friction acting on m1 and m2.c. Write three equations (one for each mass) that would allow you to determine theacceleration of the system and tensions in two strings. It is not necessary to solveequations simultaneously.4. (4 marks).Draw a free-body force diagram for block A and block B. Assume that mass of Ais larger than mass of B and that blocks move. All surfaces are rough and frictionmust be included. The pulley is frictionless. Use the following symbols todesignate forces: friction (f), normal force (N), tension (T), weight (W). Usesubscripts if two or more forces are of the same type. If necessary, use additionalsymbols to designate forces and explain their meaning. All action-reaction pairs offorces must be designated by the same symbol.5. (4 marks)A jet traveling at constant speed of 124 m/s executes a vertical loop with radius of545 m, as shown below. The mass of the pilot is 70.0 kg.Determine the magnitude of the force of the seat on the pilot at the bottom of theloop. Draw a free-body force diagram for the pilot and the direction of hisacceleration.N – Mg = ??2?N = Mg + M?2? = ? (g + ??2) = (70.0) (9.8 + 124 5452) = 2660 ?
