Problem 1 :
The temperature T in celsius in a long rod of length 10 m, insulated at both ends is the function of length x given by
T = x(10 - x)
Prove that the rate of change of temperature at the midpoint of the rod is 0.
Problem 2 :
A person learnt 100 words for an English test. The number of words the person remembers in t days after learning is given by
W(t) = 100×(1− 0.1t)^{2} , 0 ≤ t ≤10
What is the rate at which the person forgets the words 2 days after learning?
Problem 3 :
A particle moves so that the distance moved is according to the law
s(t) = t^{3}/3 - t^{2} + 3
At what time the velocity and acceleration is zero.
Problem 4 :
A particle is fired straight up from the ground to reach a height of s feet in t seconds where
s(t) = 128t - 16t^{2}
i) Compute the maximum height of the particle reached ?
ii) What is the velocity when the particle hits the ground ?
Problem 5 :
A particle moves along a horizontal line such that its position at any time t ≥ 0 is given by
s(t) = t^{3} − 6t^{2} + 9t + 1
where s is measured in meters and t in seconds?
(i) At what time the particle is at rest?
(ii) At what time the particle changes its direction?
(iii) Find the total distance travelled by the particle in the first 2 seconds.
1) So, temperature at the midpoint of the rod is 0.
2) the number of words he forgets is 16.
3) t = 1
4) i) 256 ft ii) The velocity when it reaches the ground is -128 ft/s
5) i) t = 1 and t = 3
ii) Then the particle changes its direction in between 1 to 3 seconds.
iii) 6 meters
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM