Determining distance traveled from velocity

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A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on, the following velocities are recorded: Time since breaks were applied (seconds) 0|25|5 |75 Velocity (feet per second) 61 339 0 Give lower and upper estimates (using all of the available data) for the distance (in feet) the car traveled after the brakes were applied. Lower: Upper: Suppose that a person is taking a walk along a long straight path and walks at a constant rate of 6 miles per hour. a. On the graph below, sketch a labeled graph of the velocity function v(t) = 6 9-+tmph 8t 71 6+ 51 4+ 31 21 b. How far did the person travel during the first hour, the first two hours? How is this distance related to the area of a certain region under the graph of y = v(t)? c. Use part b to sketch the graph of the position function y = s(t) (assuming that s(0) = 0.) 94miles Clear All Draw: / d. Write the function s(t) = :] e. Find the derivative of s(t). s'(t) = [: f. Compare the answer in part e and v(t). The velocity of a car is f(t) = 8t meters per second. Use a graph of f(t) to find the exact distance travelled by the car, in meters, from t = 0 to t = 8 seconds. Distance = m \fN- -10 6 103 4100 O 8 6 3 -O - v 2 4 6 2 8 10 t e. -10 6 7 9 10 11Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at = 0 and t = for the graph below. Evaluate A(z) forz =1, 2, 3, and 4. 5 4 3 2 1 A1) = A(2) = A(3) = A4) - The velocity of a particle moving along the z-axis is given by f() = 8 4 cm/sec. Use the graph of f(t) to find the exact change in position of the particle from time = 0 to = 3 seconds (including units). Change in Position = The velocities of two cars are shown in the graph. (a) From the time the brakes were applied, how many seconds did it take each car to stop? . o (b) From the time the brakes were applied, which car traveled farther until it came to a complete stop? @ Neither, they went the same distance OA OB co\\/ velocity (feet/sec) 20 40 60 time (seconds) Two cars start at the same time and travel in the same direction along a straight road. The figure below gives velocity, v (in km/hr), of each car as a function of time (in hr). The velocity of car A is given by the solid, blue curve, and the velocity for car B by the dashed, red curve. (a) Which car attains the larger maximum velocity? Car[B v|v attains the larger maximum velocity. (b) Which car stops first? Car[B V| o stops first. (c) Which car travels farther? Car|Av|vY o travels farther. Suppose an object moves along a straight line. The graph below shows the velocity of the object from t = 0 seconds to = 10 seconds. 5 Velocity ~ N W 1 2 3 4 5 Determine the intervals over which the object is moving forward, moving backward, or is stationary. Report solutions using interval notation. Over what interval(s), if any, is the object moving forward? L) Over what interval(s), if any, is the object moving backward? Over what interval(s), if any, is the object stationary? An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel from t = 0 to t = 15? OO V ur a velocity (ft/sec) N W A 5 10 15 20 25 30 35 40 45 time (sec) feetLiquid leaked from a damaged tank at a rate of r(t) liters per hour. The rate decreased as time passed and values of the rate at two-hour time intervals are shown in the table. t (hr) | r(t) (L/h) 0 10.6 N 10.3 4 9.9 6 9.6 8 9.3 10 9.0 Find lower and upper estimates for the total amount of liquid that leaked out of the tank in the first 10 hours. lower estimate = liters upper estimate = liters