Assume the equation x= At^4 +Bt^2 describes the motion of a particular object, with x having...
Assume the equation x= At^4 +Bt^2 describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. (a)determine the dimensions of constants A and B (b) then find the derivative of x in respect to t. (c) determine the dimensions of the derivative dx/dt.
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Assume the equation x= At^4 +Bt^2 describes the motion of a
particular object, with x having...
(a) Assume the equation x = At 3 +Bt describes the motion of a particular object,...
(a) Assume the equation x = At 3 +Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt = 3At 2 +B
(a) Assume the equation x = At3 + Bt describes the motion of a particular object,...
(a) Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.) (b) Determine the dimensions of the derivative dx/dt = 3At2 + B. (Use the following as necessary: L and...
Determine the dimensions of the constants A and B
a) Assume the equation x=At3+Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time.Determine the dimensions of the constants A and B.b) Determine the dimensions of the derivative dx/dt=3At2+B
2. Assume that the equation ? = ??^3 + ?? correctly describes the motion of an...
2. Assume that the equation ? = ??^3 + ?? correctly describes the motion of an object, where ? is the position (in meters) and ? is the time (in seconds). a) What units must ? and ? have? b) What are the units of the derivative ??/???
So, how do we describe diffusive motion? If a particular object moves a distance Ar from...
So, how do we describe diffusive motion? If a particular object moves a distance Ar from its original location (displacement) in a time Δ t, we cannot write down an equation that precisely relates dr and Δ, since the direction and distance moved by the object between collisions with the fluid particles is random and the time between collisions is also random. Because of these random effects, a particular object has very little chance of ever returning to the position...
Using the quantities for rotational motion, write an equation that describes spinning motion of an object,...
Using the quantities for rotational motion, write an equation that describes spinning motion of an object, for example, a record player, merry-go-round, or a rotating table in your home: a. For an object rotating at a steady speed 2. b. For an object speeding up at a steady rate c. For an object slowing down at a stcady rate
Assume that x and y are functions of t, and x and y are related by the equation y= 4x+3.
Assume that x and y are functions of t, and x and y are related by the equation y= 4x+3. (a) Given that dx/dt=1, find dy/dt when x=2. (b) Given that dy/dt=4, find dx/dt when x=3.
The motion of an object is described by the equation below. x = (0.50 m) cos(π...
The motion of an object is described by the equation below. x = (0.50 m) cos(π t / 9) (a) Find the position of the object at t = 0 and at t = 0.30 s. (b) Find the amplitude of the motion. (c) Find the frequency of the motion. (d) Find the period of the motion.
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stoc...
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic differential equation dS ơSdX+1Sdt. what stochastic differential equation does the stochastic process (a) Y 25, (b) Y = S (c) Y-es, (d) YeT-/S follow? In each cases express the coefficients of dX and dt in terms of Y rather than S. Use Ito's lemma
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic...
4. The position of an object as a function of time is given by x(t) at-bt...
4. The position of an object as a function of time is given by x(t) at-bt ct-d, where a 3.6 m/s, b 4 m/s, c = 60 m/s and d= 7 m. (a) Find the instantaneous velocity at t =24 s. (b) Find the average velocity over the first 2.4 seconds, (c) Find the instantaneous acceleration at 2.4 s, (d) Find the average acceleration over the first 2.4 seconds. (Be sure to include the correct signs) (a) and (c) are...
So, how do we describe diffusive motion? If a particular object moves a distance Ar from its original location (displacement) in a time Δ t, we cannot write down an equation that precisely relates dr and Δ, since the direction and distance moved by the object between collisions with the fluid particles is random and the time between collisions is also random. Because of these random effects, a particular object has very little chance of ever returning to the position...
Using the quantities for rotational motion, write an equation that describes spinning motion of an object, for example, a record player, merry-go-round, or a rotating table in your home: a. For an object rotating at a steady speed 2. b. For an object speeding up at a steady rate c. For an object slowing down at a stcady rate
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic differential equation dS ơSdX+1Sdt. what stochastic differential equation does the stochastic process (a) Y 25, (b) Y = S (c) Y-es, (d) YeT-/S follow? In each cases express the coefficients of dX and dt in terms of Y rather than S. Use Ito's lemma
PROBLEM 2. [5 points] Let X(t) be a Brownian motion. Assume that the stock price follows the stochastic...
4. The position of an object as a function of time is given by x(t) at-bt ct-d, where a 3.6 m/s, b 4 m/s, c = 60 m/s and d= 7 m. (a) Find the instantaneous velocity at t =24 s. (b) Find the average velocity over the first 2.4 seconds, (c) Find the instantaneous acceleration at 2.4 s, (d) Find the average acceleration over the first 2.4 seconds. (Be sure to include the correct signs) (a) and (c) are...
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