Department of Mechanical Engineering MENG 263 TUTORIAL 1 Q1. The motion of a particle is defined by the relation x 2t3 6t2 10, where x is expressed in m and t in seconds. Determine the time, position, and acceleration when v 0. ( Ans. x 2m, a 12 m/s2 ) Q2. The motion of a particle is defined by the relation x 2t3 -15t2 24t 4, where x is expressed in meters and t in seconds. Determine (a) when the velocity is zero, (b) the position and the total distance traveled when the acceleration is zero. (Ans. (a) 1s ,4s (b) 1.5m,24.5m) Q3. A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns red. The traffic light is timed to stay red for 24 s. If the motorist wishes to pass the light without stopping just as it turns green again, determine (a) the required uniform deceleration of the car, (b) the speed of the car as it passes the light. ( Ans. (a) -0.4167 m/s2 (b) 18 km/h) Q4. Automobiles A and B are traveling in adjacent highway lanes and at t 0 have the positions and speeds shown. Knowing that automobile A has a constant acceleration of 0.6 m/s2 and that B has a constant deceleration of 0.4 m/s2, determine (a) when and where A will overtake B, (b) the speed of each automobile at that time. ( Ans. xA203 m (b) vA 67.8 km/h,vB37.1 km/h) Q5. The main elevator A of the CN Tower in Toronto rises about 350 m and for most of its run has a constant speed of 22 km/h. Assume that both the acceleration and deceleration have a constant magnitude of 1g and determine the time duration t of the elevator run. ( Ans. t 59.76 s ) Q6. A motorcycle patrolman starts from rest at A two seconds after a car, speeding at the constant rate of 120 km/h, passes point A. If the patrolman accelerates at the rate of 6 m/s2 until he reaches his maximum permissible speed of 150 km/h, which he maintains, calculate the distance s from point A to the point at which he overtakes the car. (Ans. s 912m) Q7. Ball A is released from rest at a height of 12 m at the same time that a second ball B is thrown upward 1.5 m from the ground. If the balls pass one another at a height of 6 m, determine the speed at which ball was thrown upward. ( Ans. vB 9.5 m/s) Q8. A motorcycle starts from rest at t 0 and travels along a straight road with the speed shown by the v-t graph. Determine the total distance the motorcycle travels until it stops when t 15 s. Also plot the a-t graphs. ( Ans. S 52.5 m ) Q9. The cable and pulley system is used to lift the load A. Determine the speed of A if the end C of the cable is given an upward speed of 2 m/s. ( vA 0.666 m/s up ) Q10. Determine the time needed for the load at B to attain a speed of 8 m/s, starting from rest, if the cable is drawn into the motor with an acceleration of 0.2 m/s. (Ans. t160 s) ( Ans. (a) vo 9.62 m/s up (b) v 29.62 m/s down ) f 6tPioJauF8Mk/kj0 GV5ZTFf3UyC7f890UlKDkqq( pcCsOwEDf)67TO1e@/ T R38fu j2 hjXsBv-X@t)r1

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