Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. the time t is measured in seconds and the units for r(t) are tonnes (metric tons) per second. (use 6 equal subintervals.) t 0 1 2 3 4 5 6 r(t) 2 8 20 38 42 54 60 (a) give upper and lower estimates for the total quantity q(6) of erupted materials after 6 seconds. q(6) = tonnes (lower estimate) q(6) = tonnes (upper estimate) (b) use the midpoint rule to estimate q(6). (use 3 equal subintervals.) q(6) = tonnes

Learning goal: to understand newton's 1st law. newton's principia states this first law of motion: an object subject to no net force maintains its state of motion, either at rest or at constant speed in a right line. this law may be restated as follows: if the sum of all forces acting on an object is zero, then the acceleration of that object is zero. mathematically this is just a special case of the 2nd law of motion, f⃗ =ma⃗ , when f⃗ =0. when studying newtonian mechanics, it is best to remember the 1st law in two ways: if the net force (i.e., sum of all forces) acting on an object is zero, the object will keep moving with constant velocity (which may be zero). if an object is moving with constant velocity, that is, with zero acceleration, then the net force acting on that object must be zero. complete the following sentences to see if you can apply these ideas. part a if a car is moving to the left with constant velocity, one can conclude that