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HW3 Close Grading Policy [x] Grading Policy Number of answer attempts per question is: 6 You gain credit for: Correctly answering a question in a Part You lose credit for: Exhausting all attempts or giving up on a question in a Part or Hint Incorrectly answering a question in a Part Late submissions: receive no credit. Hints are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions.There is no penalty for leaving questions in Hints unanswered. Grading of Incorrect Answers before the last attempt: You lose 100%/(# of options - 1) credit per incorrect answer on multiple-choice and true/false questions. You lose 3% credit per incorrect answer on questions that are not multiple-choice or true/false. An Object Accelerating on a Ramp Learning Goal: Understand that the acceleration vector is in the direction of the change of the velocity vector. In one dimensional (straight line) motion, acceleration is accompanied by a change in speed, and the acceleration is always parallel (or antiparallel) to the velocity. When motion can occur in two dimensions (e.g. is confined to a tabletop but can lie anywhere in the x-y plane), the definition of acceleration is in the limit . In picturing this vector derivative you can think of the derivative of a vector as an instantaneous quantity by thinking of the velocity of the tip of the arrow as the vector changes in time. Alternatively, you can (for small ) approximate the acceleration as . Obviously the difference between and is another vector that can lie in any direction. If it is longer but in the same direction, will be parallel to . On the other hand, if has the same magnitude as but is in a slightly different direction, then will be perpendicular to . In general, can differ from in both magnitude and direction, hence can have any direction relative to . This problem contains several examples of this.Consider an object sliding on a frictionless ramp as depicted here. The object is already moving along the ramp toward position 2 when it is at position 1. The following questions concern the direction of the object's acceleration vector, . In this problem, you should find the direction of the acceleration vector by drawing the velocity vector at two points near to the position you are asked about. Note that since the object moves along the track, its velocity vector at a point will be tangent to the track at that point. The acceleration vector will point in the same direction as the vector difference of the two velocities. (This is a result of the equation given above.) Position, Velocity, and Acceleration Learning Goal: To identify situations when position, velocity, and /or acceleration change, realizing that change can be in direction or magnitude. If an object's position is described by a function of time, (measured from a nonaccelerating reference frame), then the object's velocity is described by the time derivative of the position, , and the object's acceleration is described by the time derivative of the velocity, . It is often convenient to discuss the average of the latter two quantities between times and : and . A Wild Ride A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the x axis be parallel to the ground and the positive y axis point upward. In the time interval from to s, the trajectory of the car along a certain section of the track is given by , where is a positive dimensionless constant. Direction of Acceleration of Pendulum Learning Goal: To understand that the direction of acceleration is in the direction of the change of the velocity, which is unrelated to the direction of the velocity. The pendulum shown makes a full swing from to . Ignore friction and assume that the string is massless. The eight labeled arrows represent directions to be referred to when answering the following questions.

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