Linear Motion

 

 

In this activity we look at motion in one dimension.  Some of this you are familiar with, such as the equation distance = speed x time.   Acceleration, on the other hand, is a new concept for most students, and it is easy to form misconceptions about it.  Be careful not to make the mistake of thinking of what the velocity will do when you are asked to describe the acceleration.

 

1.      Let’s first make sure you do understand d = vt.

(a)    How far will a car go in 5 hours if it is travelling at 30 miles per hour?

 

 

 

(b)    How long does it take a bullet to travel 600 m at 400 m/s?

 

 

 

 

2.      What is the “natural” state of motion according to Aristotle?  According to Galileo?

 

 

 

 

 

3.      As shown in the text, if a body has a constant acceleration “a”, then the distance it travels in a time “t” is given by d = ½ at2.  Use this formula to find how far a ball will fall in 5 seconds.  Use a = g = 10 m/s2.  (Actually, g is 9.8 m/s2, but the approximation is a good one and makes calculations much simpler.)

 

 

 

4.  Measuring acceleration.  We will do a little experiment here to measure the acceleration of a cart rolling down an incline.  The experiment is straightforward: We will release the cart from a point a distance d from the bottom of the incline, and use a stopwatch to measure the time it takes the ball to reach the bottom.  We will do this for several different values of the distance d, and then graph the data to check our formula and find the acceleration.

 

 

 


                                                     d

 

 


Use the metal ramp and the cart with it.  Choose at least 4 different distances d, ranging from the full length of the ramp to as small as you can measure comfortably with the stopwatch.  Make a table with your data (d and t). 

 


  d            t  

 

 

 

 

 

 

 


Since the acceleration is a constant, and d = ½ at2, we will graph d versus t2.  “d” will be on the “y” axis, and “t2” on the “x” axis.  Is your graph a straight line?  If so, use a straightedge to fit a straight line to your data, and then find the slope.

             y

 

                                                   t2

 

 

 

 

 

In this case, the slope is (½ a).  What then is the acceleration “a”?

 

 

 

 

5.  If I throw a ball up into the air, it will come back down to me.  What is its acceleration at the top of its arc?