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Exam 3: Motion in Two or Three Dimensions

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Question 21

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Basic kinematics variables: If an object is accelerating toward a point, then it must be getting closer and closer to that point.

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Question 22

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Basic kinematics variables: The figure shows the graph of the position x as a function of time for an object moving in the straight line (the x-axis) . Which of the following graphs best describes the velocity along the x-axis as a function of time for this object?

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Question 23

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Free fall: A rock is thrown directly upward from the edge of the roof of a building that is 66.2 meters tall. The rock misses the building on its way down, and is observed to strike the ground 4.00 seconds after being thrown. Neglect any effects of air resistance. With what speed was the rock thrown?

Basic kinematics variables: The figure shows the position of an object (moving along a straight line) as a function of time. Assume two significant figures in each number. Which of the following statements about this object is true over the interval shown?

Basic kinematics variables: If the acceleration of an object is negative, the object must be slowing down.

Constant acceleration: A dragster starts from rest and travels 400 m in 6.70 s with constant acceleration. What is its velocity when it crosses the finish line?

Basic kinematics variables: When can we be certain that the average velocity of an object is always equal to its instantaneous velocity?

Free fall: To determine the height of a flagpole, Abby throws a ball straight up and times it. She sees that the ball goes by the top of the pole after 0.50 s and then reaches the top of the pole again after a total elapsed time of 4.1 s. How high is the pole above the point where the ball was launched? (You can ignore air resistance.)

Basic kinematics variables: If the graph of the position as a function of time for an object is a horizontal line, that object cannot be accelerating.

Basic kinematics variables: An object is moving in a straight line along the x-axis. A plot of its velocity in the x direction as a function of time is shown in the figure. Which graph represents its acceleration in the x direction as a function of time?

Free fall: A rocket takes off vertically from the launchpad with no initial velocity but a constant upward acceleration of 2.25 m/s². At 15.4 s after blastoff, the engines fail completely so the only force on the rocket from then on is the pull of gravity. (a) What is the maximum height the rocket will reach above the launchpad? (b) How fast is the rocket moving at the instant before it crashes onto the launchpad? (c) How long after engine failure does it take for the rocket to crash onto the launchpad?

Free fall: A package is dropped from a helicopter moving upward at If it takes before the package strikes the ground, how high above the ground was the package when it was released if air resistance is negligible?

Constant acceleration: A ball rolls across a floor with an acceleration of 0.100 m/s² in a direction opposite to its velocity. The ball has a velocity of 4.00 m/s after rolling a distance 6.00 m across the floor. What was the initial speed of the ball?

Constant acceleration: A car is 200 m from a stop sign and traveling toward the sign at 40.0 m/s. At this time, the driver suddenly realizes that she must stop the car. If it takes 0.200 s for the driver to apply the brakes, what must be the magnitude of the constant acceleration of the car after the brakes are applied so that the car will come to rest at the stop sign?

Basic kinematics variables: An object is moving with constant non-zero acceleration along the +x-axis. A graph of the velocity in the x direction as a function of time for this object is

Constant acceleration: An object starts from rest at time t = 0.00 s and moves in the +x direction with constant acceleration. The object travels 12.0 m from time t = 1.00 s to time t = 2.00 s. What is the acceleration of the object?

Basic kinematics variables: The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t = 0. At time T, what is true about these two vehicles since time t = 0?

Free fall: At the same moment from the top of a building 3.0 × 10² m tall, one rock is dropped and one is thrown downward with an initial velocity of . Both of them experience negligible air resistance. How much EARLIER does the thrown rock strike the ground?

Basic kinematics variables using calculus: The velocity of an object as a function of time is given by v(t) = 2.00 m/s + (3.00 m/s²) t - (1.0 m/s³) t². Determine the instantaneous acceleration of the object at time t = 4.00 s.

Basic kinematics variables using calculus: The position of an object is given by where and x and t are in SI units. What is the instantaneous acceleration of the object when