1. An object moves along the `x` axis according to the equation `x = 3.00t^2 - 2.00t + 3.00`, where `x` is in meters and `t `is in seconds. Determine
(a) the average speed between `t = 2.00 s` and `t = 3.00 s`,
(b) the instantaneous speed at `t = 2.00 s` and at `t = 3.00 s`,
(c) the average acceleration between `t = 2.00 s` and `t = 3.00 s`, and
(d) the instantaneous acceleration at `t = 2.00 s` and `t = 3.00 s`.
(e) At what time is the object at rest?
View Detail ... 2. Figure P2.15 shows a graph of `v_x` versus `t` for the motion of a motorcyclist as he starts from rest and moves along the road in a straight line.
(a) Find the average acceleration for the time interval `t = 0` to `t = 6.00 s`.
(b) Estimate the time at which the acceleration has its greatest positive value and the value of the acceleration at that instant.
(c) When is the acceleration zero?
(d) Estimate the maximum negative value of the acceleration and the time at which it occurs.
View Detail ... 3. At `t = 0`, one toy car is set rolling on a straight track with initial position `15.0 cm`, initial velocity `-3.50 cm//s`, and constant acceleration `2.40 cm//s^2`. At the same moment, another toy car is set rolling on an adjacent track with initial position `10.0 cm`, initial velocity `+5.50 cm//s`, and constant acceleration zero.
(a) At what time, if any, do the two cars have equal speeds?
(b) What are their speeds at that time?
(c) At what time(s), if any, do the cars pass each other?
(d) What are their locations at that time?
(e) Explain the difference between question (a) and question (c) as clearly as possible.
View Detail ... 4. A particle moves along the x axis. Its position is given by the equation `x=2+3t -4t^2`,with `x` in meters and `t` in seconds. Determine
(a) its position when it changes direction and
(b) its velocity when it returns to the position it had at `t = 0`.
View Detail ... 5. A package is dropped at time `t = 0` from a helicopter that is descending steadily at a speed `v_i`.
(a) What is the speed of the package in terms of `v_i, g`, and `t`?
(b) What vertical distance `d` is it from the helicopter in terms of `g` and `t`?
(c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed?
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