Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
mperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 38 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object. (a) dT dt = $$ Correct: Your answer is correct. 0.4(38-T) Suppose the ambient temp TA(t) = 38cos( π 30 t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature T of the object. (b) dT dt = Correct: Your answer is correct. If we measure time in hours the differential equation in part (b) changes. What is the new differential equation? Use the letter s to denote time in hours. (c) dT ds = If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation? Use the letter F to denote temperature in degrees Fahrenheit.
1 answer:
You might be interested in
Answer:
C. Impulse = F*t=(m*a)*t= m*(a*t) = m*Dv= D(Momentum) (“D” here’s mean Delta so change in)
Explanation:
In fact, the impulse is equal to the change in momentum of an object.
Impulse is defined as the product between the force (F) and the time (t):
however, the force is defined as the product between mass (m) and acceleration (a):
But the product a (acceleration) times t (time) is equal to the change in velocity of the object:
And this is exactly the definition of change in momentum: