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A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. The motion of the car is defined by the position
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Vector Mechanics For Engineers
- A car P travels along a straight road with a constant speed v = 64 mi/hr. At the instant when the angle 0 = 60°, determine the values of r in ft/sec and 8 in deg/sec. Assume = 113! Answers: r = 1 0 = F MI x חומון V ft/sec deg/secarrow_forwardAn automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular trackarrow_forward1- A particle moves along the x axis. Its position varies with time according to the expression x=-41+ 2f where x is in meters and t is in seconds. The position-time graph for this motion is shown in Figure. Note that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment 1 = 1 s, and moves in the positive x direction at times /> 1 s. (A) Determine the displacement of the particle in the time intervals t=0 to 1=1 s and t= 1 s to / = 3 s. B) Calculate the average velocity during these two-time intervals C) determine the instantaneous velocity and instantaneous speed at t= 0.5 s. x(m) Slope = 4 m/s 10 00 8 9 10 O Slope =-2 m/s 1 2 015 t(s)arrow_forward
- Two cars A and B are stopped at a traffic light, waiting for the light to change from red to green, see Figure 3. Car B is 6 meters behind car A. When the light changes to green, car A leaves accelerating at a rate of 0.3 m / sec2, while car B departs 2 seconds later and accelerates at a rate of 0.8 m / sec2. Determine the position where they are next to each other, measured from the “o” point.arrow_forwardQuestion 2 [2/105]: A car P travels along a straight road with a constant speed v = 65 mi/hr. At the instant when the angle 0 = 60°, determine the values of r in ft/sec and è in deg/sec. 100' y 1 1 Ve O -x 15 Varrow_forwardThe velocity of a boat relative to a fixed-earth coordinate system is 12 m/s and is constant. The length of the tow rope is 15 m. The angle ߠ is 30° and is increasing at the rate of 10°/s. What are the velocity and acceleration of the skier relative to the boat?arrow_forward
- 11.7 A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. She drives the car in a straight line so that the x coordinate is defined by the relation x(1) = 0.5r - 3r + 3t + 2, where x and t are expressed in meters and seconds, respectively. Determine (a) when the velocity is zero, (b) the position and total distance travelled when the acceleration is zero.arrow_forwardProblem 2: Determine the equations of motion for the system shown to the right in terms of the given coordinates. kat x2 2r WE m r k I k 0 WWE ww k ܠܠ X1arrow_forwardFor the section shown of a race track, the two race cars travel atconstant speeds. At the instant shown, the front ends of both carscross lineCCat the same time. For the curved section (θ= [θ]°,r1= [r1]m, andr2= [r2]m), both drivers drive at the maximumspeed that their car and tyres allow. Consequently, the maximumlateral (sideways) acceleration of carsAandBare [k1]gand [k2]grespectively whereg=9.81 m/s2. When the second car (notnecessarily carB) crosses lineDD, how far is it behind the firstcar? Assume the race track is straight afterDDand both carsmaintain their speeds. Ignore the horizontal distance between thecars.arrow_forward
- Newton's Third Law states that: The velocity of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. The acceleration of a particle is proportional to the vector sum of forces acting on it, and is in the direction of this vector sum. The forces of action and reaction between interacting bodies are equal in magnitude, opposite in direction, and collinear. O A particle remains at rest or continues to move with a uniform velocity if there is no unbalanced force acting on it. 7arrow_forwardQuestion 7 A particle which moves with curvilinear motion has coordinates in millimeters which vary with the time t in seconds according to x = 6.1t2 - 6.1t and y = 6.5t2 - t3/ 2.5. Determine the magnitudes of the velocity v and acceleration a and the angles which these vectors make with the x-axis when t = 3.5 s.Answers: When t = 3.5 s,arrow_forwardTwo objects moving along x-axis are starting at the same time. Their positions are measured in centimeters at time t in seconds. If the equation of motion of objects 1 and 2 are and respectively, determine the distance between the objects at the instant when they have the same velocity. 2 cm 4 cm 3 cm 1 cmarrow_forward
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