Midterm1_key

# Midterm1_key - 1 A truck initially at rest at a trafﬁc...

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Unformatted text preview: 1. A truck, initially at rest at a trafﬁc light, speeds up with a constant acceleration a a 0.4 m/sz. A police car passes the same trafﬁc light 12 s after the truck departed. If the police car is traveling at a constant speed of 30 m/s: (at) How long does the police car need to overtake the truck? (10 points) (b) How far from the trafﬁg light will the police car overtake the truck? (10 points) :05 ' al‘géﬁll C03 twoim : 13.53 _.]f2,g :2 M85 3 (b) *5 = Va (4:425 =(30m1g§t(t.lSs§: B'HtSm 2. (a) The movement of an object is described by the following equation: x(t) = -t +2t3, Where t is in seconds and x in meters. Calculate: (i) The average velocity from t = 1 s to t = 5 s. (5 points) (ii) The acceleration of the car at t = 2 s. (5 points) . g 2 g ~ i :::J (t) \icwa :2 w : .-._....._._.——~——q ”2113 m :EGIMIg ' 6 3 ~ g )(f6): —6+2‘5O m : 293m XilD-ﬁ -i+?,: lm QJ 2am: pd: cm vac): JG: ~I+ét a. as) ”CT-F ‘GLC2332 QLIIMK'Z) (b) A particle moves with constant speed around the circle below. When it is at point A its coordinates are x = -3 m, y a 0 m and its velocity is 6 j m/s. Obtain its velocity and acceleration at point B. (Express your answer in terms of unit vectors). (1 0 points) (315 1; \l: 3; 26 mag: = legz y': "€73: Ge mm R 397: L00 CQuJN‘iPQ 3? >< 3. A hiker makes three consecutive displacements across a dense forest starting from his campsite. The ﬁrst displacement is 5 km due North, the second one 3 km 30° South of East, and the third one 7 km 10° North of West. Find: (a) How far from its original position will the hiker end? (”pom“) (b) In which direction should he walk to go back to his campsite? (10 points) '§ 0 d3 (-3—? (0% lo 1‘ +?gsm\0" ABkn’ (co If; at gr :r liw—G‘WH’ZSWW :: \+ 'Z, -}— 3 = Masher?) km (a) o Km (b) ‘f’a-g ".' ﬁlm: 4. A projectile ﬁred into the air from ground level lands 40 m away ﬁom the launching position 5 5 later. Neglecting air resistance, ﬁnd: ' (a) Direction of the initial velocity. (5 points) (b) Magnitude of the initial velocity. (5 points) (0) Maximum height reached by the projectile during its ﬂight. (10 points) 5. The two blocks in the diagram below are connected by a massless cord to a massless pulley. The masses of the blocks are: M1= 2 kg, M2: 5 kg. The coefﬁcient of kinetic friction between M1 and the incline plane IS 0.1. /—‘> Mmewﬁ (3) Draw the force diagram. (4 points) __ . (b) Calculate the acceleration of the system. (8 points) ' {L (0) Obtain the tension on the cord. (8 points) ...
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