### 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, v_{0}.

#### 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.

#### Answer

(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 / time^{2}. We have
observed that some students will mindlessly give an answer of 9.81 m/s^{2} 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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