Problem 2.6 The position of a particle is given byr = 2t (meters), 0 = 5t (radians). (a) Plot the path of the particle. (b) Obtain an expression for the speed as a function of time. Answers: (a) This is the spiral of Archimedes. (b) v = (4+ 100t? )1/2 m/s.
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- 1. 3.A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation. (a) Calculate the average speed of the blade tip in the helicopter's frame of reference. (b) What is its average velocity over one revolution? 2. Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain. 3. A commuter backs her car out of her garage with an acceleration of (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.800 s, what is her decelerationIn an experiment, a shearwater (a seabird) was taken from its nest, flown a distance 5120 km away, and released. It found its way back to its nest 12.5 days after release. Part A If we place the origin in the nest and extend the +x-axis to the release point, what was the bird's average velocity for the return flight? Express your answer in meters per second. ANSWER: Vay.-x = m/s Part B What was the bird's average velocity for the whole episode, from leaving the nest to returning? Express your answer in meters per second. ANSWER: Vav. = m/sThe Beretta Model 92S (the standard-issue U.S. army pistol) has a barrel 127 mmmm long. The bullets leave this barrel with a muzzle velocity of 349 m/sm/s. 1) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer in meters per second squared. 2) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer as a multiple of acceleration due to gravity g. 3) For how long is the bullet in the barrel? Express your answer in seconds.
- A cat walks in a straight line, which we shall call the -axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Figure 1). I. Calculate the area under the graph between t = 0 and t = 6.0 s. (Express your answer to two significant figures and include the appropriate units.) II. For the time interval t = 0 to t = 6.0 s, what is the magnitude of the average velocity of the cat? (Express your answer to two significant figures and include the appropriate units.) III. Use constant-acceleration equations to calculate the distance the cat travels in this time interval. (Express your answer to two significant figures and include the appropriate units.)The path of motion of a 7-lblb particle in the horizontal plane is described in terms of polar coordinates as rr = (2 tt ++ 1)ftft and θθ = (0.5 t2t2 −− tt) radrad, where tt is in seconds.How would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)
- I need part B answered in this question.1.1 Let's say a cart's position is given by x(t) at3 – Bt. (1) - Assume the constants, a and B, are positive. (a) What must be the general type of unit (like length, mass, time, and combinations of these) for each of the constants, a and B? (b) Draw, by hand, a sketch of the two functions at and –ßt for t > 0. Add the two curves graphically to get a final sketch of x(t). (c) Calculate the cart's velocity vr and acceleration ar. (d) Find an expression for the time t = to at which the cart is momentarily at rest. Check: If a and B had the values 1 and 27, respectively (in the correct SI units), you would find t = 3 s. (e) Give the expression for the cart's position x(to) at the time t = to. Always simplify your answer, - and confirm that the units are correct.Hi, below is the explanation to the problem cited. But I don't understand the answer to the last question #3: Determine its average acceleration during the 34.0 sec interval. I am lost; can you help? Thanks! A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABCis 214 m, and the car completes the turn in 34.0 s. An x y coordinate system is shown. Three points A, B, and C are shown on the graph. These points are joined by a dotted curve. Point A is on the negative y-axis, point C is on the positive x-axis, while point B is in the fourth quadrant IV at an angle of −35° with the x-axis. From point A the curve initially moves rightward along a circular path, curves upward to cross B and then meets C. An arrow indicating the velocity at point A points horizontally and to the right. An arrow indicating the velocity at point C points vertically upward. 1. What is the acceleration when the car is at…