2. The following raph shows p-the x component of the objects velocky, as a funct

Question

2. The following raph shows p-the x component of the objects velocky, as a function of fre. Vx (ms) TMEt (see) Use this graph to answer the folowing A) When is the object at rest? When is it moving in the x direction? When is it moving in the - x direcion? B) When is the object speeding up? When is it slowing down? When is it reversing its direction of motion? C) When is the thing moving the fastest? D) When is the object's acceleraton vector pointng in the - x direction and when in the+ x direction? E) When do the objoct's accoloration and velocity vectors point in opposito directions? F) When do the object's acceleration and velocity vectors paint in the same direction? G) When is the object not accelerating? At these times, is the object moving? H) When is the object not moving? Is its acceleration zero at these times? l) When is the thing: speeding up while moving in the- x direction? slowing down whle moving in + x dir.? B- 12 5. A spacecraft travels along a straight line. The position of the spacecraft is given as a function of time by where x is in feet and t is in seconds. a) Find the average velocity of the spacecraft over the interval from 0 to t = 1 sec.

Explanation / Answer

How to tell if the object is speeding up or slowing down? Speeding up means that the magnitude (or numerical value) of the velocity is getting large. For instance, an object with a velocity changing from +3 m/s to + 9 m/s is speeding up. Similarly, an object with a velocity changing from -3 m/s to -9 m/s is also speeding up. In each case, the magnitude of the velocity (the number itself, not the sign or direction) is increasing; the speed is getting bigger. Given this fact, one would believe that an object is speeding up if the line on a velocity-time graph is changing from near the 0-velocity point to a location further away from the 0-velocity point. That is, if the line is getting further away from the x-axis (the 0-velocity point), then the object is speeding up. And conversely, if the line is approaching the x-axis, then the object is slowing down.

5a) X= 4-24t^2-8t^3

Rate of change of distance, dx/dt = -48t-24t^2

At t=0, velocity = 0

At t=1, velocity= -72

Average velocity= 72/2= 36 m/s

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