Chapter 1
Exercises
1. The speeds are the same, but their velocities are not. Velocity includes both rate of travel and direction. Since their directions are different so are their velocities.
3. An object moving in a circle at constant speed undergoes (constant) acceleration, since its direction is changing. By definition acceleration is the change in velocity over time. If there is no change in velocity, velocity is constant, there is no acceleration.
6. Only the second (middle) hill will speed increase while acceleration decreases. The more level (flatter) the surface the lower the acceleration will become.
7. The streaks are the result of the downward motion of the rain and the sideways motion of the car. The 45° angle suggest the rain and car are moving at the same speed (and velocity?).
9. Acceleration is 0 since there is no change in velocity. Recall the definition of acceleration.
13. The rate of change of speed is the same, about 10 m/s2, whether going up or down. As a result, the time spent going up is the same as the time spent going down.
14. Both strike the ground with the same speed. When the ball thrown up returns to ground level its speed is the same as when it was thrown up, which is the same as the ball that was thrown down.
17. If not for air resistance, rain drops would strike the ground with bullet like speed.
Problems
2. -10 km/h.s
5. Using g = 10 m/s2, we see that velocity = gravity * time; v = 10 m/s2 * 10 s = 100 m/s. Average velocity = (beginning vel. + final vel.)/2 = (0 + 100 m/s)/2 = 50 m/s downward.
distance = average vel. * time; d = 50 m/s * 10 s = 500 m. What other formula may be used to find distance?
6. velocity = gravity * time; v = 10 m/s2 * 8 s = 80 m/s.
the distance fallen is 1/2 * g * t2; d = (1/2)*( 10 m/s2)*(82) = 320 m.
7. Acceleration = (change in velocity)/(time); a = (50 m/s - 0)/(10 s) = 5 m/s2.
8. Recall velocity = gravity * time and distance = (1/2)*gravity*time2.
In one second, how fast = 20 m/s, how far = 10 m. These values are twice what we would see no earth.