### Kinematics Problem 8.1.3

#### Description

A ball moves across the screen with constant acceleration. Values near +/- 4.5 are effective. This problem is one of the most effective kinematics problems. The animation should start at time t = 0 with the trajectory set so that the ball is off the left or right hand side of the screen. That is, the ball should not be visible at t = 0 and move onto the grid at some later time. Many students simply cannot do a problem that does not give them an easy way to determine a value for the initial velocity, v0

#### Question

(a) What is the acceleration of the ball? You may click-drag the mouse inside the animation at any time to measure position. Start

(b) What is the average velocity from time t = 1.0 to t = 3.0? What is the average acceleration? You may click-drag the mouse inside the animation at any time to measure position.

(a) Determined by the script. For example, the line in the script document.Animator.addObject("circle","r=10,x=16*t,y=18*t-4*t*t"); will display a ball with an acceleration of 8 units / time2. We have observed that some students will mindlessly give an answer of 9.81 m/s2 if the problem is recast to show vertical motion. This problem is an effective tool for discussing measurement error since a straightforward application of v = Dx / Dt will likely give incorrect values due to the difficulty of measuring the center of the ball using the mouse. Even good students can disagree about the correct result. Students should be required to obtain an answer that is correct to better than 2 percent.

(b) Determined by the script as in a. Different students may be assigned different time intervals in order to make the point that instantaneous and average acceleration have the same value if the acceleration is constant.

#### Reference

See Giancoli-PA: 2-7, Giancoli-SE: 2-7.

#### Credits

Physlet problem authored by Mario Belloni.

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