Figure 2-17 gives the acceleration a(t) of a Chihuahua as it chases a German shepherd along an axis. In which of the time periods indicated does the Chihuahua move at constant speed?
Chihuahua moves with constant speed during the time period E
The graph is shown in figure 2.17
The concept used to solve this problem is constant speed and acceleration. The acceleration is the rate of change of velocity. Acceleration is a vector quantity. If speed is constant and its direction is not changing then there will be no acceleration.
The acceleration can be written as,
This implies that the velocity is constant.
It means that to find out the time period that has a constant speed, we need to find the time period that has zero acceleration. From the given graph it can be seen that only time period E has zero acceleration. For all the other time periods, the acceleration is increasing, decreasing, positive or negative.
Thus, it can be concluded that Chihuahua moves with constant speed during the time period E.
The position of an object moving along an x axis is given by , where x is in metres and t in seconds. Find the position of the object at following values of t: a) 1sec ,(b) 2sec, (c) 3sec, and (d) 4sec, (e) What is the object’s displacement between t=0 and t=4sec ? (f) What is its average velocity for the time interval from t=2s to t=4s? (g) Graph x vs t for and indicate how the answer for f can be found on the graph.
Figure 2-45 shows a simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right in Fig. 2-45. You then position your thumb and forefinger at the other dot (on the left in Fig. 2-45), being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time. (a) How far from the lower dot should you place the mark? How much higher should you place the marks for (b) , (c) , (d) , and (e) ? (For example, should the marker be 2 times as far from the dot as the marker? If so, give an answer of 2 times. Can you find any pattern in the answers?
In an arcade video game, a spot is programmed to move across the screen according to, where x is distance in centimeters measured from the left edge of the screen and role="math" localid="1656154621648" is time in seconds. When the spot reaches a screen edge, at either or , t is reset to and the spot starts moving again according to . (a) At what time after starting is the spot instantaneously at rest? (b) At what value of x does this occur? (c) What is the spot’s acceleration (including sign) when this occurs? (d)Is it moving right or left just prior to coming to rest? (e) Just after?(f) At what time does it first reach an edge of the screen?
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