1. A truck accelerates from rest, on horizontal ground, and its speed as a function of time follows the equation 15t - 2t2. Once the truck reaches maximum speed, it maintains a constant speed for another 4 minutes. At this point the truck decelerates to a stop at a constant rate and the magnitude of its acceleration is 2 m/s^2.
(a) What is the maximum speed the truck attains and
(b) at what time does this occur?
(c) How far does the truck travel during the entire trip?
2. Astronauts on a distant planet toss a rock into the air. With the aid of a camera that takes pictures at a steady rate, they record the height of the rock as a function of time as given in the table below.
(a) Find the average velocity of the rock in the time interval between each measurement and the next.
(b) Using these average velocities to approximate instantaneous velocities at the midpoints of the time intervals, make a graph of the velocity as a function of time. Does the rock move with constant acceleration? Ifo, plot a straight line of best. It on the graph and calculate its slope to find the acceleration. Microsoft Excel may be useful for this problem.
3. (a) Find the position vector, as a function of radius r, for points A, B, and C, using origin 0.
(b) Find the change in position vector from A to B and B to C using origin 0.
(c) Repeat parts (a) and (b) using origin 0? What can you conclude about the location of the origin in reference to the (d) position vectors and (e) changes in the position vectors?
| Height of a Rock versus Time |
| Time(s) |
Height(m) |
Time(s) |
Height(m) |
| 0 |
5 |
2.75 |
7.62 |
| 0.25 |
5.75 |
3 |
7.25 |
| 0.5 |
6.4 |
3.25 |
6.77 |
| 1 |
7.38 |
3.75 |
5.52 |
| 1.25 |
7.72 |
4 |
4.73 |
| 1.5 |
7.96 |
4.25 |
3.85 |
| 1.75 |
8.1 |
4.5 |
2.86 |
| 2 |
8.13 |
4.75 |
1.77 |
| 2.25 |
8.07 |
5 |
0.58 |
| 2.5 |
7.9 |
|
|