Practice: A moving box's motion is described by the velocity graph below. The box's initial position is x = 0.

(a) How far has the box moved at t = 4?

(b) What is the displacement of the box from t=4 to t=10?

Subjects

Sections | |||
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Vectors, Scalars, & Displacement | 14 mins | 0 completed | Learn |

Average Velocity | 33 mins | 0 completed | Learn |

Intro to Acceleration | 8 mins | 0 completed | Learn |

Position-Time Graphs & Velocity | 26 mins | 0 completed | Learn |

Conceptual Problems with Position-Time Graphs | 22 mins | 0 completed | Learn |

Velocity-Time Graphs & Acceleration | 6 mins | 0 completed | Learn |

Calculating Displacement from Velocity-Time Graphs | 15 mins | 0 completed | Learn |

Conceptual Problems with Velocity-Time Graphs | 11 mins | 0 completed | Learn |

Calculating Change in Velocity from Acceleration-Time Graphs | 11 mins | 0 completed | Learn |

Graphing Position, Velocity, and Acceleration Graphs | 11 mins | 0 completed | Learn |

Kinematics Equations | 53 mins | 0 completed | Learn |

Vertical Motion and Free Fall | 20 mins | 0 completed | Learn |

Catch/Overtake Problems | 23 mins | 0 completed | Learn |

Additional Practice |
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Motion Diagrams |

Proportional Reasoning |

Concept #1: Calculating Displacement from Velocity-Time Graphs

Practice: A moving box's motion is described by the velocity graph below. The box's initial position is x = 0.

(a) How far has the box moved at t = 4?

(b) What is the displacement of the box from t=4 to t=10?

0 of 3 completed

Concept #1: Calculating Displacement from Velocity-Time Graphs

Practice #1: Displacement of a Moving Box

Example #1: Displacement of a Car

Figure 2.2 shows the velocity time graph of a motorist during a 8 second period. The motorist leaves home (position x = 0m) at time t = 0s and the velocity change as shown. How far does the motorist travel during the first 6 seconds?

Consider the plot describing motion along a straight line with an initial position of 10 m. What is the position at 9 seconds?
1. 30.0
2. 24.0
3. 49.0
4. 42.0
5. 29.0
6. 31.5
7. 12.0
8. 17.0
9. 41.0
10. 21.5

A somewhat idealized graph of the speed of the blood in the ascending aorta during one beat of the heart appears as in Figure P2.16. a. Approximately how far, in cm, does the blood move during one beat? b. Assume similar data for the motion of the blood in your aorta, and make a rough estimate of the distance from your heart to your brain. Estimate how many beats of the heart it takes for blood to travel from your heart to your brain.

To describe the motion of a particle along a straight line, it is often convenient to draw a graph representing the position of the particle at different times. This type of graph is usually referred to as an x x vs. t t graph. To draw such a graph, choose an axis system in which time t t is plotted on the horizontal axis and position x x on the vertical axis. Then, indicate the values of x x at various times t t . Mathematically, this corresponds to plotting the variable x x as a function of t t . An example of a graph of position as a function of time for a particle traveling along a straight line is shown below. Note that an x x vs. t t graph like this does not represent the path of the particle in space.PART AWhat is the overall displacement ΔxΔx of the particle?PART BWhat is the average velocity vavvav of the particle over the time interval Δt=50.0sΔt=50.0s ?Express your answer in meters per second.PART CWhat is the instantaneous velocity vv of the particle at t=10.0st=10.0s?Express your answer in meters per second.Another common graphical representation of motion along a straight line is the vv vs. tt, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time tt is plotted on the horizontal axis and velocity vv on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In straight-line motion, however, these vectors have only one nonzero component in the direction of motion. Thus, in this problem, we will call vv aa the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion.PART DWhich of the graphs shown is the correct vv vs. tt plot for the motion described in the previous parts?

A car in stop-and-go traffic starts at rest, moves forward 21 m in 8.0 s, then comes to rest again. The velocity-versus-time plot for this car is given in the figure.A) What distance does the car cover in the first 4.0 seconds of its motion?B) What distance does the car cover in the last 2.0 seconds of its motion?C) What is the constant speed V that characterizes the middle portion of its motion?

Two cars travel on the parallel lanes of a two-lane road. The cars are at the same location at time t=0s, and move in such a way as to produce the velocity (relative to the ground) vs. time graph shown in the figure. (Figure 1)On the graph, one vertical block is equivalent to one velocity unit.Rank car #1's speed relative to the ground at the lettered times (A through E).Rank from largest to smallest. To rank items as equivalent, overlap them.

Two cars travel on the parallel lanes of a two-lane road. The cars are at the same location at time t=0s, and move in such a way as to produce the velocity (relative to the ground) vs. time graph shown in the figure. (Figure 1)On the graph, one vertical block is equivalent to one velocity unit.Rank the distance between the cars at the lettered times.Rank from largest to smallest. To rank items as equivalent, overlap them.

The graph in the figure shows the velocity v of a sports car as a function of time t. Find the distance d0,2 traveled by the car between t = 0s and t = 2s.

The object maintains a zero velocity A. for 1 second. B. for more than a second. C. for less than a second but more than an instant. D. only for an instant.

Part A. What is the amplitude of the oscillation? Express your answer to three significant figures and include the appropriate units.Part B. What is the phase constant? Express your answer in radians as positive number. Express your answer to three significant figures. Part C. What is the position at t = 0 s? Express your answer to three significant figures and include the appropriate units.

How far does the runner whose velocity-time graph is shown in the figure travel in 16 s? The vertical scaling is set by vs= 8.0 m/s.

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