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
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(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...
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.
(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
1. (10pts) The speed v of an object is given by the equation v = At3...
1. (10pts) The speed v of an object is given by the equation v = At3 - Bect where t refers to time. (a) What are the dimensions of A, B, and C? (6) What are the SI units for the constants A, B and C? 2. (7pts) What units and value do the following combination of the two fundamental constants of nature (that is €o = 8.85 x 10-12 m-3 kg-1st AP and Mo = 1.26 x 10-6 m...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the nega...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
1-5 Dimensional analysis is a powerful way to check the results of a physics calculation 41....
1-5 Dimensional analysis is a powerful way to check the results of a physics calculation 41. One equation that describes motion of an object is where x is the position of the object, a is the acceleration, t is time, vo is the initial speed, and xo is the initial position. Show that the dimensions in the equation are consistent.
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B=...
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B=...
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
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 ??/???
1. (10pts) The speed v of an object is given by the equation v = At3 - Bect where t refers to time. (a) What are the dimensions of A, B, and C? (6) What are the SI units for the constants A, B and C? 2. (7pts) What units and value do the following combination of the two fundamental constants of nature (that is €o = 8.85 x 10-12 m-3 kg-1st AP and Mo = 1.26 x 10-6 m...
Let's consider a function described in terms of its displacement y(x,t) at t 0 by: where a, b and e are positive constants a) Write an expression for this wave profile, having a speed in the negative x-direction, as a function of position and time (b) Sketch the profile of the wave at t-0 s and t 2 s if v1 m/s (c) Determine if the following functions describe a travelling wave: (i) vr,t) (ar+ bt c), where a, b...
1-5 Dimensional analysis is a powerful way to check the results of a physics calculation 41. One equation that describes motion of an object is where x is the position of the object, a is the acceleration, t is time, vo is the initial speed, and xo is the initial position. Show that the dimensions in the equation are consistent.
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
(b) Consider the matrix differential equation for the vector x(t) d dt - B2+ where B= (69) 4 10 5 -1 (i) Find a particular solution to the matrix differential equation. (ii) Evaluate exp(Bt). (iii) Find the general solution to the matrix differential equation. Express the general solution in terms of the components of the vector (0).
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
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