Relating Position, Velocity, and Acceleration Graphs

Check the following link for some solutions to the handout problems.

Problem 7. B and D, the velocity is zero.

Problem 8. Again, at B, D, and E, the object is at rest since the tangent line is horizontal.

Problem 9. Area under the velocity vs. time graph is 640 m.

Problem 10.
a) Moving faster means the speed (or absolute value of the slope) is greater. The slope is greater for object b.
b) Object A has an initial position that is greater than the initial position of object B. As a result, we can define it to be "ahead".
c) The intersection represents when the objects are at the same position, or when they meet.

HW from Textbook: Pages 41 - 46, Questions 5, 18, 19 and Problems 39, 58, 59, and 61
Solutions:
Questions:
5. yes - to win, the car must reach the finish line in the shortest possible time, NOT at the largest possible speed. A car could drive slowly for a while, and then suddenly accelerate at the end to move faster than the other cars.
18. constant positive velocity for 20 seconds, speeding up in positive direction for 15 seconds, slows down and stops at at t = 38 seconds, turns around and speeds up until 45 seconds, and then slows down to a stop at t = 50 seconds.
19. Constant acceleration from t = 0 to 50 seconds, reaches its highest speed at t = 50 seconds, and then slows down and stops from t = 90 to 105 seconds. it then speeds up a bit. Notice that the object NEVER turns around - its velocity is always the same sign.

Problems
39. If we define down to be positive, then the velocity vs. time graph will look like a straight line with positive slope equal to the acceleration of gravity. The position vs. time graph will be a parabola that opens upwards.

58. Check back later for this.

59.
a) negative direction (negative slope)
b) speeding up - the velocity is becoming more negative.
c) negative - the velocity is becoming more negative.
d) positive direction (positive slope)
e) speeding up - slope is becoming more positive.
f) positive - slope is becoming more positive
g) object is not moving from C to D, so its velocity is constant and zero, and therefore acceleration is zero.

61. six times the distance as on Earth