Question

In: Math

. [4 pts] The temperature of a 4 foot metal rod at a point x feet...

. [4 pts] The temperature of a 4 foot metal rod at a point x feet from its left endpoint is given by T(x) = 1 + 3x 2 , 0 ≤ x ≤ 4, where T is measured in degrees Celsius (and x is measured in feet). Find the average temperature of the rod.

5. [6 pts] A particle moves along a coordinate line and has an acceleration given by a(t) = 4t+ 6 cm/sec2 . If the particle’s initial velocity is v(0) = −2 cm/sec, and its initial position is s(0) = 4 cm, find its position function s.

Solutions

Expert Solution


Related Solutions

Ant on a metal plate. The temperature at a point ( x, y) on a metal...
Ant on a metal plate. The temperature at a point ( x, y) on a metal plate is T(x, y) = 4x2 - 4xy + y2 . An ant on the plate walks around the circle of radius 10 centered at the origin. a) What are the highest and lowest temperatures encountered by the ant? b) Suppose the ant has changed its trajectory and is walking around the circle of radius 5. Is the highest temperature encountered by the ant...
The temperature , u(x,t), in a metal rod of length L satisfies           del u/ del...
The temperature , u(x,t), in a metal rod of length L satisfies           del u/ del t = k del squared u / del x squared limit 0 less than or equal to, x less than or equal to L , t greater than or equal to 0 The ends of the rod at x=0 and x=L , are maintained at a constant temperature T not 0 , so that the boundary conditions are                 u(0, t) =0    u(L, t)...
As the temperature of a metal rod varies, so does the resistance and the dimensions of...
As the temperature of a metal rod varies, so does the resistance and the dimensions of the rod. If a copper rod has a resistance of 4.78 Ω at 20.0°C, determine the resistance of the rod (in Ω) at 120°C by accounting for the changes in both the resistivity and the dimensions of the rod. The coefficient of linear expansion for copper is 1.67 ✕ 10−5 (°C)−1 and the temperature coefficient of resistivity is 4.04 ✕ 10−3 (°C)−1.
We have a metal rod of length L. The rod is on the x-axis extending from...
We have a metal rod of length L. The rod is on the x-axis extending from 0 to L. We select a point X on the rod randomly and uniformly and cut the rod at X. This gives two smaller rods of lengths X and L − X. We select the longer piece (if the two pieces are of equal length we select one of them) and cut it again randomly and uniformly to get three pieces. What is the...
A metal rod at 38°C is placed in a room at a constant temperature of 0°C....
A metal rod at 38°C is placed in a room at a constant temperature of 0°C. (a) If after 20 minutes the temperature of the rod is 20°C, find the temperature function T(t) that models the temperature T of the rod at time t. Assume Newton's Law of Cooling. Note: You must state the differential equation that models this situation and include how to solve this DE as part of your solution. (b)Determine the time it will take for the...
Question 1: Consider a metal rod of uniform temperature. Is it possible that heat spontaneously flow...
Question 1: Consider a metal rod of uniform temperature. Is it possible that heat spontaneously flow from one end of the rod to the other end so that they end up in different temperatures? Why? Question 2: The ocean is full of heat energy. Explains what limits people from using this energy to make electricity? Question 3: The density of water is about 1,000 kg/m3, and 1 mole of water molecules has a mass of 18 grams. Calculate the hidden...
To what temperature (in °C) must a cylindrical rod of one metal 10.045 mm in diameter...
To what temperature (in °C) must a cylindrical rod of one metal 10.045 mm in diameter and a plate of second metal having a circular hole 9.990 mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is 25°C and that the linear expansion coefficient values for metals one and two are 4.9 x 10-6 (°C)-1 and 17 x 10-6 (°C)-1, respectively.
Find an expression for the temperature u(x,t) in a rod of length π, if the diffusivity...
Find an expression for the temperature u(x,t) in a rod of length π, if the diffusivity (k) is 1, the ends x= 0 and x=π are both thermally insulated and the initial temperature is given by u(x,0) ={2x/π , 0 < x < π/2} u(x,0) ={1 , π/2 < x < π}
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached...
A 4 foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium through which the mass moves offers a damping force numerically equal to 2^1/2 times the instantaneous velocity. Find the equation of motion if the mass is initially released from the equilibrium position with a downward velocity of 9 ft/a. (Use g =32 ft/s^2 for the acceleration due to gravity.) a) Find the time at which the mass attains its extreme...
(1 point) The temperature at a point (x,y,z) is given by ?(?,?,?)=200?−?2−?2/4−?2/9, where ? is measured...
(1 point) The temperature at a point (x,y,z) is given by ?(?,?,?)=200?−?2−?2/4−?2/9, where ? is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (1, 1, 1) in the direction toward the point (-1, -1, -1). In which direction (unit vector) does the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT