If a single constant force acts on an object that moves on a straight line
If a single constant force acts on an object that moves on a straight line, the object's velocity is a linear function of time. The equation v=vi + at gives its velocity v as a function of time, where a is its constant acceleration. What if velocity is instead a linear function of position? Assume that as a particular object moves through a resistive medium, its speed decreases as described by the equation v = vi-vx, where k is a constant coefficient and x is the position of the object. Find the law describing the total force acting on this object. (Enter an expression for the magnitude of the total force. Use the following as necessary: m, k, and v.)
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If a single constant force acts on an object that moves on a straight line
5. (15 pts] A force acting on an object is proportional to the square root of...
5. (15 pts] A force acting on an object is proportional to the square root of the distance the object moves. The equation for the distance r is: 19 = kyr, for some constant k. The object starts at t=0 with position r = 0 and velocity v = 0. The object moves four meters in the first second. That is, r(t = 1) = 4. (a) Find the object's velocity as a function of position, v(r). (b) Find the...
Work through the mathematics of how a constant force acting on an object, in one dimension,...
Work through the mathematics of how a constant force acting on an object, in one dimension, will affect the velocity as a function of time and the position as a function of time (definite integrals will be involved). Then combine the results for position and velocity to derive the relationship between position and speed for an object that moves in one dimension with a constant force (hint: algebraically eliminate time). What situation(s) might this theory describe?
3. A 0.5 kg object moves along a straight line. The net force acting on the...
3. A 0.5 kg object moves along a straight line. The net force acting on the object varies with its displacement as shown by the graph on the next page. The object starts from rest at x = 0 and travels a total distance of 20 m. 5 4 Force 2 6 8 10 1214 16 18 2022 Displacement (m) each of the following: (a) the acceleration of the object at x-6 m (b) the time needed for the object...
At one instant, force F 4.7i N acts on a 0.374 kg object that has position...
At one instant, force F 4.7i N acts on a 0.374 kg object that has position vector (7.80-7.80f) m and velocity vector V - (-1.11+1.11K) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b) the torque acting on the object?
A force moves an object in the direction of the force. The graph shows the force...
A force moves an object in the direction of the force. The graph shows the force versus the object's position (a) Find the work done when the object moves from 0 to 2.0 m. (b) If the mass of this object is 1.5 Kg and it started from rest find the final velocity at 2.0 m.
6) At one instant, force F 4.0j N acts on a 0.25 kg object that has...
6) At one instant, force F 4.0j N acts on a 0.25 kg object that has position vector (2.0-2.0k) m and velocity vector (-50i+5.0k) m/s. About the origin and in unit vector notation, what are (a) the object's angular momentum and (b) the torque acting on the object?
2. A mass moves along a straight line, which we will call the x-axis with the...
2. A mass moves along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 40.00cm + 16.00 en/s t-10.00cm/s2 t2 A. Find the object's initial velocity, initial position, and initial acceleration. B. At what time t is the velocity of the object zero? C. How long after starting does it take the object to return to its starting point?...
6. A 2.0-kg object moves in a straight line on a horizontal frictionless surface. The graph...
6. A 2.0-kg object moves in a straight line on a horizontal frictionless surface. The graph above shows the velocity of the object as a function of time. The various equal time intervals (sections) are labeled using Roman numerals: I, II, III, IV, and V. The net force on the object always acts along the line of motion of the object Which section(s) of the graph correspond to a condition of zero net force? a. b. Which section(s) of the...
A single, nonconstant force acts in the +?+x direction on an 5.06 kg5.06 kg object that...
A single, nonconstant force acts in the +?+x direction on an 5.06 kg5.06 kg object that is constrained to move along the ?x‑axis. As a result, the object's position as a function of time is ?(?)=?+??2+??4?=7.38 m?=4.57 m/s2?=0.478 m/s4x(t)=A+Bt2+Ct4A=7.38 mB=4.57 m/s2C=0.478 m/s4 How much work is done by this force from ?=0 st=0 s to ?=2.34 s?
Question 9 You should be able to answer this question after studying Unit 8. An object moves along a straight line, and its speed v (in metres per second) when at a position r (in metres) from its st...
Question 9 You should be able to answer this question after studying Unit 8. An object moves along a straight line, and its speed v (in metres per second) when at a position r (in metres) from its starting point can be modelled by the differential equation 10 marks 0 dr0, 20), where k is a positive constant (a) Find the general solution of this differential equation in explicit form (b) The speed of the object at its starting point...
5. (15 pts] A force acting on an object is proportional to the square root of the distance the object moves. The equation for the distance r is: 19 = kyr, for some constant k. The object starts at t=0 with position r = 0 and velocity v = 0. The object moves four meters in the first second. That is, r(t = 1) = 4. (a) Find the object's velocity as a function of position, v(r). (b) Find the...
3. A 0.5 kg object moves along a straight line. The net force acting on the object varies with its displacement as shown by the graph on the next page. The object starts from rest at x = 0 and travels a total distance of 20 m. 5 4 Force 2 6 8 10 1214 16 18 2022 Displacement (m) each of the following: (a) the acceleration of the object at x-6 m (b) the time needed for the object...
At one instant, force F 4.7i N acts on a 0.374 kg object that has position vector (7.80-7.80f) m and velocity vector V - (-1.11+1.11K) m/s. About the origin and in unit- vector notation, what are (a) the object's angular momentum and (b) the torque acting on the object?
A force moves an object in the direction of the force. The graph shows the force versus the object's position (a) Find the work done when the object moves from 0 to 2.0 m. (b) If the mass of this object is 1.5 Kg and it started from rest find the final velocity at 2.0 m.
6) At one instant, force F 4.0j N acts on a 0.25 kg object that has position vector (2.0-2.0k) m and velocity vector (-50i+5.0k) m/s. About the origin and in unit vector notation, what are (a) the object's angular momentum and (b) the torque acting on the object?
2. A mass moves along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t) = 40.00cm + 16.00 en/s t-10.00cm/s2 t2 A. Find the object's initial velocity, initial position, and initial acceleration. B. At what time t is the velocity of the object zero? C. How long after starting does it take the object to return to its starting point?...
6. A 2.0-kg object moves in a straight line on a horizontal frictionless surface. The graph above shows the velocity of the object as a function of time. The various equal time intervals (sections) are labeled using Roman numerals: I, II, III, IV, and V. The net force on the object always acts along the line of motion of the object Which section(s) of the graph correspond to a condition of zero net force? a. b. Which section(s) of the...
Question 9 You should be able to answer this question after studying Unit 8. An object moves along a straight line, and its speed v (in metres per second) when at a position r (in metres) from its starting point can be modelled by the differential equation 10 marks 0 dr0, 20), where k is a positive constant (a) Find the general solution of this differential equation in explicit form (b) The speed of the object at its starting point...
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