It moves at constant speed v. At time t₂ = 3 s, the particle's acceleration is a₂ = 31-7ĵ m/s². What are the speed v and the radius r of the path taken by the particle if t₂t₁ is less than one period? (Hint: get the angle between ₁ and ₂ first)
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- The force F has a magnitude of 590 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. Assume F = 590 N, 0 = 31° Answers: F = (i Fx= i Fy || IM F i+ N N Mi INAn object travels in a vertical circle of 1.43 m radius. When the object is traveling downward and is 28.0° from its lowest point, its total acceleration is a = (18.51 + 16.2ĵ) m/s². At this instant, determine the following. (Take the angle 28.0° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.) esc 7 (a) magnitude of the radial acceleration m/s² (b) magnitude of the tangential acceleration m/s² (c) speed of the object m/s (d) velocity of the object (Express your answer in vector form.) m/s v= 1 ² F1 Q A 1 N 2 Q F2 W S 3 X # H option command 80 F3 E D $ 4 C 990 GOD F4 R F % 67 8 5 F5 V T MacBook Air 6 G F6 Y B & 7 H 4 F7 U N 00 * 8 J FB 1 ( 9 M F9 K O O < A I -10 L || ! P V F11 1 + { [ 2 412 1 - option commandYou can use the formula for centripetal acceleration OR You have to calculate the average acceleration directly from the definition, a = delta v / delta t. You have to first get a_x by using the velocity's initial and final x components, do a_y from the y components, and then use the Pythagorean formula to get the magnitude of the acceleration vector.
- The Moon orbits the Earth in an approximately circular path. The velocity of the moon as a function of time is given by:vx = −v sin(?t)vy = v cos(?t)where v = 945 m/s and ? = 2.46 10-6 radians/s. What is the average acceleration of the Moon over the following time intervals? For each, give the magnitude and direction as an angle measured counterclockwise from the positive x-axis.(a) from t = 0 to t = 0.200 daysmagnitude ______m/s2direction ______° counterclockwise from the +x-axis (b) from t = 0 to t = 0.0020 daysmagnitude ______m/s2direction ______° counterclockwise from the +x-axisWe know that the moon Callisto revolves around Jupiter during a period of 17.0 days.17.0 days. The average distance from the center of Jupiter to the center of Callisto is 1.95×109 m.1.95×109 m. What is the acceleration ?a of Callisto due to its motion around Jupiter?Your answer is partially correct. A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one instant, it moves through the point at coordinates (4.90 m, 3.70 m) with a velocity of -2.40 î m/s and an acceleration of +11.9 m/s². What are the (a) x and (b) y coordinates of the center of the circular path? (a) Number i 4.41 (b) Number i 3.70 Unit Unit m m
- The average distance of the earth from the sun is about 1.5 x 108 km (Figure 1). Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system. (a) Estimate the speed of the earth as it moves in its orbit around the sun. Express your answer in miles per hour with the appropriate number of significant figures. (b) Estimate the angle between the position vector of the earth now and what it will be in 4 months. (c) Calculate the distance between these two positions.According to Los Angeles Air Traffic Control, an Air Force SR-71 has a constant velocity of 1942 knots (999 m/s) along the negative y direction, and a Navy F-18 has an acceleration of 4 m/s^2 along the positive x direction (both of these are fighter jets). What is the acceleration of the F-18 as measured by an observer in the SR-71 (in m/s^2)? [i and j represent unit vectors along the x and y directions respectively]A rotating fan completes 1180 revolutions every minute. Consider the tip of a blade, at a radius of 20.0 cm. (a) Through what distance does the tip move in one revolution? What are (b) the tip's speed and (c) the magnitude of its acceleration? (d) What is the period of the motion? (a) Number i Units (b) Number i Units
- A particle of mass m has a time-dependent position vector r(t) = (Rcos(ωt),Rsin(ωt),αt) in Cartesian coordinates, where R, ω and α are positive constants. What are the physical dimensions of R, ω and α? Show that the speed of the particle is constant. Does it mean that the acceleration is zero? Justify.3.1A particle moves on the xy plane in a circle centered at the origin. At some point the particle speed and acceleration are 6.0i m/s and (3.0i + 4.0j) m/s2 respectively. What are the x and y coordinates of the particle at this time?