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Hnd the parametregutions for a lineamente ancientation Question An object travels at a steady rate along...
For this question, we are concerned with the movement of an object along a path in the plane. We are assuming that the plane is a coordinate plane and the object starts at the point. As the object mo...
For this question, we are concerned with the movement of an object along a path in the plane. We are assuming that the plane is a coordinate plane and the object starts at the point. As the object moves along the path, each point on that path has two coordinates. The coordinates depend on the distance traveled along the path. Let us call this distance S, the length of the path from the origin to a point P on the...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at))....
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
Practice Problems 12-12. Determine the total time required for a car to travel 1km along a...
Practice Problems 12-12. Determine the total time required for a car to travel 1km along a straight road if it starts from rest (position 1), reaches a maximum speed at some intermediate point (position 2) and then stops at the end of the road (position 3). The car accelerates at 1.5m/s2 and decelerates at 2m/s. Hint: Draw a straight line with three positions marked on it. Write kinematics equations corresponding to positions 1-2 and 2-3, and solve the resulting equations...
12-10. Car A starts from rest at t-0 and travels along a straight road with a...
12-10. Car A starts from rest at t-0 and travels along a straight road with a constant acceleration of 3 m/s until it reaches a speed of 27 m/s. Afterwards it maintains this speed. Also, when-0, car B located 2000 m down the road is traveling towards A at a constant speed of 20 m/s. Determine the distance travelled by car A when they pass each other. 20 m/s 2000 m 12-11. A particle travels along a straight line with...
When an object is dropped straight down, the distance in feet) that it travels in t...
When an object is dropped straight down, the distance in feet) that it travels in t seconds is given by s(t) = - 1612. Find the velocity at each of the following times. a. After 2 seconds. b. After 6 seconds. c. After 10 seconds. d. Find the acceleration. a. The velocity after 2 seconds is ft/sec. Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives. y = x2...
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...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 +...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
1 In a disastrous first flight, an experimental paper airplane follows the trajectory indicated by these...
1 In a disastrous first flight, an experimental paper airplane follows the trajectory indicated by these parametric equations: x(t) = 1 - 3 sint y(t) = 4 - 3 cost but crashes into a wall after 10 seconds. Give all coordinates as (x,y) coordinates, along with their associated t values. The (x,y) simply gives you the location of the plane. The x-axis can be assumed to be the ground. You could consider the y values to be in feet, so...
1.2 A non-stop freight train leaves Edinburgh for London at 6:00 and travels at a steady 75mph (t...
please answer both question
1.2 A non-stop freight train leaves Edinburgh for London at 6:00 and travels at a steady 75mph (time taken to accelerate is negligible) for the 332 miles. A passenger train leaves at 7:00 and travels at 126 mph (again time taken to accelerate is minimal) however it stops every SOmins for a period of 10 minutes before continuing In a table show the distance that each train has travelled at each hour into the journeys Plot...
7. General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s...
7.
General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i- 9j + 2k)m, and s3 (10i 8j -k)m. a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b)...
For this question, we are concerned with the movement of an object along a path in the plane. We are assuming that the plane is a coordinate plane and the object starts at the point. As the object moves along the path, each point on that path has two coordinates. The coordinates depend on the distance traveled along the path. Let us call this distance S, the length of the path from the origin to a point P on the...
The velocity vector of an object is given by y(t) = (* sin(at), 1, a cos(at)). Assume that at t = 1, the object is at the point P(1,1,0). (a) Find the position vector F(t) of the object. (b) Find parametric equations of the line which is tangent to r(t) at P. (c) Find the distance that the object traveled from the point t = 0 to t = 1. (d) Find an equation for the normal plane of r(t)...
Practice Problems 12-12. Determine the total time required for a car to travel 1km along a straight road if it starts from rest (position 1), reaches a maximum speed at some intermediate point (position 2) and then stops at the end of the road (position 3). The car accelerates at 1.5m/s2 and decelerates at 2m/s. Hint: Draw a straight line with three positions marked on it. Write kinematics equations corresponding to positions 1-2 and 2-3, and solve the resulting equations...
12-10. Car A starts from rest at t-0 and travels along a straight road with a constant acceleration of 3 m/s until it reaches a speed of 27 m/s. Afterwards it maintains this speed. Also, when-0, car B located 2000 m down the road is traveling towards A at a constant speed of 20 m/s. Determine the distance travelled by car A when they pass each other. 20 m/s 2000 m 12-11. A particle travels along a straight line with...
When an object is dropped straight down, the distance in feet) that it travels in t seconds is given by s(t) = - 1612. Find the velocity at each of the following times. a. After 2 seconds. b. After 6 seconds. c. After 10 seconds. d. Find the acceleration. a. The velocity after 2 seconds is ft/sec. Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives. y = x2...
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...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
1 In a disastrous first flight, an experimental paper airplane follows the trajectory indicated by these parametric equations: x(t) = 1 - 3 sint y(t) = 4 - 3 cost but crashes into a wall after 10 seconds. Give all coordinates as (x,y) coordinates, along with their associated t values. The (x,y) simply gives you the location of the plane. The x-axis can be assumed to be the ground. You could consider the y values to be in feet, so...
please answer both question
1.2 A non-stop freight train leaves Edinburgh for London at 6:00 and travels at a steady 75mph (time taken to accelerate is negligible) for the 332 miles. A passenger train leaves at 7:00 and travels at 126 mph (again time taken to accelerate is minimal) however it stops every SOmins for a period of 10 minutes before continuing In a table show the distance that each train has travelled at each hour into the journeys Plot...
7.
General Motion with Unit Vectors and Components An object undergoes the following consecutive displacements: s (2i +3j +5k)m,s2 (6i- 9j + 2k)m, and s3 (10i 8j -k)m. a) Find the resultant displacement in terms of unit vectors and components. b) State the magnitude of the resultant displacement. 2. Suppose a hiker travels 5 km southwest from their camp. Then, the hiker travels 2 km 75° north of east. a) Find the displacement of the hiker form their camp. b)...
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