1. a) Acceleration is simply a change in velocity.
    b) During acceleration, an object travels farther during successive, equal time intervals, i.e., its
        displacements increase during successive, equal time periods.
2. Acceleration is a vector quantity and so needs both magnitude and direction.
3. a) Acceleration is measured in m/s².
    b) Recall that velocity is measured in m/s.
    c) The difference in units occurs because acceleration refers to changes in velocity (m/s) per change
        in time (s), i.e., m/s/s or m/s².
4. Acceleration has a negative value when the object is speeding up in a negative direction or is
    decelerating. Of course, the sensations felt by the occupants of a car in these two situations are quite
    different.
5. a) i) speed is constant ii) velocity is constant iii) acceleration is 0.
    b) i) speed increases ii) + velocity increases iii) + acceleration is occurring.
    c) i) speed increases ii) - velocity increases iii) - acceleration is occurring.
    d) i) speed decreases ii) - velocity decreases iii) - deceleration is occurring.
    e) i) speed decreases ii) + velocity decreases iii) + deceleration is occurring.
6. A time - position plot of:
   a) uniform velocity is a straight line with a + slope.
   b) uniform acceleration is a smooth upward concave curve of increasing slope (steepness.)
   c) uniform deceleration is a smooth upward convex arc of decreasing slope (steepness.)
7. A time - position graph for:
   a) a jet landing jet is a smooth upward convex arc of decreasing steepness.
   b) a sprinter is two phase: a smooth upward concave arc leading into a straight line with a + slope.
8. a) Acceleration is measured as m/s².
    b) The slope of a time - position graph yields the velocity not the acceleration. Recall that the unit
        of the slope for a time - position graph is m/s. Note, however, that one can infer acceleration
        from time - position graph slopes.
    c) The slope of a time - velocity graph is the acceleration value itself. The unit of the slope is m/s/s
        or m/s².
9. a) A time - velocity plot of:
        i) uniform velocity is a straight horizontal line.
        ii) uniform acceleration is a straight line with a + slope.
        iii) uniform deceleration is a straight line with a - slope.
    b) A time - velocity graph for:
        i) a jet landing jet is a straight line with a - slope.
        ii) a sprinter is two phase: a straight line rising from the origin that then flattens.
10. a) If an object moves with uniform acceleration, it will have just that one acceleration value, not a
         range.
      b) Recall that the time - velocity graph for such a situation is a straight line; as such, it will have only
          one slope.
      c) Of course, if the object moves with changing acceleration, its time - velocity graph will be a
          curve made of an infinite number of short straight segments, each one a slightly different
          slope, i.e., a slightly different acceleration value.
11. a) Although the time - position graph for acceleration is an upward concave arc and one can find an
          instantaneous slope, it would still be an instantaneous velocity and still not the object's
          acceleration. Again, one can infer acceleration information from a sequence of instantaneous
          velocity slopes.
      b) The slopes of time - velocity graphs for accelerated motion yield the acceleration values
          themselves.   Recall that a time - velocity graph for uniform acceleration is a straight line with a
          single slope (a single acceleration) while changing acceleration is described by an arc with a
          sequence of instantaneous slopes (a sequence of instantaneous accelerations.)
12. a) Wherever the plot is steep, the acceleration is i) greatest. Where the plot is less steep, the
          acceleration is ii) less.
      b) Because the driver lets up on the gas during the short time when she shifts into a higher gear,
          there are short periods of reduced acceleration.
      c) Only a related pair of velocities and times are needed to find an average acceleration during a
           certain time frame.
13. a) This graph describes an object moving with a uniform acceleration.
      b) Displacement is calculated by finding the area under the curve.
14. a) It is more correct to speak of the bubble staying in place as the cart moves forward, under it.
      b) When the bubble remains in the center of the level, the cart will be moving at a constant velocity,
          i.e., no acceleration.
15. a) Gravity causes the ball to uniformly accelerate as it descends, hence its displacements increase
          during the successive equal time intervals.
      b) The equation: d = vt + ½ gt mostly directly relates to the changing displacements as the ball
          descends.
16. a) A map of the ball's flight would be a line straight up and down.
      b) Since the launch and landing points are the same, the person's hand, the ascent and descent
          times are the same.
      c) Again, since the launch and landing points are the same, the person's hand, the ascent and
          descent distances are the same.
17. a) A more detailed plot might represent the person holding the ball out horizontally, lowering and
          then flinging it upward.
      b) An extension of the plot might represent the ball stopping in the person's raised hand which is
          then lowered and is motionless.
18. a) The lift off path of a spacecraft carries it up and away from the launch pad in an arc, moving with
          the earth's rotation.
      b) The arc shape of the spacecraft's liftoff path takes advantage of the huge, but unfelt, momentum
          given to it by the earth's rotation. In effect, the earth helps fling the craft up into space. A vertical
          liftoff would use more fuel to propel the craft to the same speed and altitude. To take maximum
          advantage of the earth's momentum, a launch pad would be close to the equator since the waist
          of the earth spins faster than the poles.