Problem 6. (10 pts) The velocity of an object v(t) at several data points is given...
Math 1300: Calculus I Project: Riemann Sums 1. A girl is running at a velocity of 12 feet per second for 10 seconds, as shown in the velocity graph below. v(t) 12 10 6 t 7 10 How far does she travel during this time? This distance can be depicted graphically as a rectangle. Shade such a rectangle and explain why it gives the distance. 2. Now the girl changes her velocity as she runs. Her velocity graph is approximately...
An object has a velocity given by v(t) = { + 20 (in ft/sec) after t seconds. Estimate the total distance traveled by the object on the interval (2, 10) using a left hand sum with n=
6.) Given the following v vs t graph for some object, the object at some velocity in the +x direction. After 3.8 seconds it stops, at 7.6 seconds it changes acceleration, and after 10 seconds, it is stopped again. (Note that from 0 s until 7.6 seconds, the acceleration is the same.) From 0 until 10 seconds, the average speed of the object is 28 m/s. What is the acceleration from 0 to 7.6 seconds in m/s2? If in the...
(10 pts) Suppose an object moves along a line with velocity v(t) = 3+- 18t +24, for 0 st < 5, where t is measured in seconds and velocity have unit of ft/s. (a) Determine when the motion is in the positive direction and when it is in the negative direction. (b) Find the displacement of the object on the interval 0 st 35. (c) Write down an expression for the distance traveled by the object over the interval 0...
Suppose the velocity V in meters per second) of a runner during the first few seconds of e race is given by t ins 0.5 11.5 2 2.5 V in m/s0 4 8.515.119 25 in the tv endpoint approximation and width 0.5 Plot these points in the plane. Sketch the velccity curve. Estimate the distance traveled by the runner by estimating the area under the velocity curve; use rectangles with heights given by a right endpoint approximation and width plane....
(1) (5 Points) The velocity of an object moving along a line is given by v(t) = 12-36 +2. Find the total distance traveled by the object during the interval of time 0 St <3.
5.1.15 Question Help The velocity of an object moving along a line is given by v 2t+4 ft/s on the interval 0sts4. a. Divide the interval [0, 4] into subintervals, [0, 1], [1, 2], [2, 3], and [3, 4]. On each subinterval, assume the object moves at a constant velocity equal to the value ofv evaluated at the midpoint of the subinterval and use these approximations to estimate the displacement of the object on [0, 4]. (See part (a) of...
1) (25 pts) Given the following table of velocity data t (s) v(m/s) a) (6 pts) Estimate the position at 2 seconds (use 1/3 Simpson's rule) b) (6 pts) Estimate the acceleration at 2 seconds (use first order centered finite difference) c) (6 pts) Estimate the position at 3 seconds (use 3/8 Simpson's rule ) d) (7 pts) Estimate the acceleration at 3 seconds (use first order centered finite difference) 7 5 0 1 2 3 4 3 3.5 4...
please help with problem (6) Use the following graph of the velocity function v(t) of an moving in a straight line to answer the following questions (a) Find the displacement of the object between t = 0 and t = 5. (b) FInd the distance traveled by the object between t = 0 and t = 5 (c) What is the position of the object at t = (d) Sketch the graph of s(t) assuming s(0) = 3. Your graph...
The graph of the velocity v(t) of an object is given below. Over which time interval did the object travel the least distance? - - -- - - + -- +--- + § 10 12 + 14 N Graph of v(t) o [0,2] O [2,8) O [8, 12] (12, 14]