Problems - Choose any 1. Two particles start at the origin on the s-axis at time t = 0 s and move along the s-axis. Their movement can be expressed by the following equations. s(t) = 1 - 3t a. When will the two points have the same speed? b. When will the two points have the same position? s (1)=91-12 c. What are the respective velocities of the points when they have the same position? 2. Suppose the population (in thousands) of a certain species of insect after 1 months is described by the function P(t) = 4t+ 100t 1 + 400 3. Let the function s(t) = 5 x +500. Determine the maximum population in the first three months. +10x + 15 represent the motion of a toy car as it travels near a sensor. At what time I will the car's distance from the sensor be the greatest? What is its velocity when the car is at that point? Describe the motion of the car after that time t. 4. Express 18 as a sum of two positive numbers whose product of the first and square of the second is as large as possible. Explain why this is the largest possible product. 5. An isosceles triangle has a vertex at the origin. Determine the area of the largest such triangle that is bound by the function x +6y= 48 and explain why this is in fact the maximum area. 6. A fireman has to reach a burning building. Determine the length of the shortest ladder that will reach over a 2 metre high fence to the burning building which is 1 metre behind the fence. 7. Car A is 40 km east of Car B and begins moving west at 40 km/h. At the same moment, Car B begins to move north at 70 km/h. What is the closest distance in kilometres the cars will be from each other and at what time t, in hours, will that distance occur? 8. A woman wants to construct a box whose base length is twice the base width. The material to build the top and bottom is $9/m and the material to build the sides is $6/m. If the woman wants the box to have a volume of 70 m, determine the dimensions of the box (in metres) that will minimize the cost of production. What is the minimum cost? 9. A document is to contain 80 square centimetres of print. The margins at the top in bottom of the document are each 2 centimetres wide and the margins on each side are 3 centimetres wide. What should be the dimensions (in centimetres) of print so that a minimum amount of paper is used?