Kinematics 1 Dimensional Kinematics Average vs Instantaneous Speed

  • Slides: 13
Download presentation
Kinematics 1 -Dimensional Kinematics

Kinematics 1 -Dimensional Kinematics

Average vs. Instantaneous Speed • • The speedometer of a car reveals information about

Average vs. Instantaneous Speed • • The speedometer of a car reveals information about the instantaneous speed of your car; that is, it shows your speed at a particular instant in time. Average speed is a measure of the distance traveled in a given period of time; it is sometimes refered to as the distance per time ratio

The Stoplight • • A blue car moving at a constant speed of 10

The Stoplight • • A blue car moving at a constant speed of 10 m/s passes a red car that is at rest. This occurs at a stoplight the moment that the light turns green. The clock is reset to 0 seconds and the velocity-time data for both cars are collected and plotted. The red car accelerates from rest at 4 m/s/s for three seconds and then maintains a constant speed. The blue car maintains a constant speed of 10 m/s for the entire 12 seconds. Observe the motion and make meaning of the accompanying graphs to answer the following questions: What is the final velocity of a car that accelerates from rest at 4 m/s/s for three seconds? What is the displacement of each individual car after three seconds (consider a kinematic equation or the area of the velocity-time graph)? What is the slope of the line for the red car for the first three seconds? What is the displacement of each individual car after nine seconds (use the area of the velocity-time graph)? Does the red car pass the blue car at three seconds? If not, then when does the red car pass the blue car? When lines on a velocity-time graph intersect, does this mean that the two cars are passing by each other? If not, what does it mean?

Positive Velocity and Positive Acceleration • • • An object which moves in the

Positive Velocity and Positive Acceleration • • • An object which moves in the positive direction has a positive velocity. If the object is speeding up, then its acceleration vector is directed in the same direction as its motion (in this case, a positive acceleration). The "ticker tape" shows that each consecutive dot is not the same distance apart (i. e. , a changing velocity) The position-time graph shows that the slope is changing (meaning a changing velocity) and positive (meaning a positive velocity). The velocity-time graph shows a line with a positive (upward) slope (meaning that there is a positive acceleration); the line is located in the positive region of the graph (corresponding to a positive velocity). The acceleration-time graph shows a horizontal line in the positive region of the graph (meaning a positive acceleration).

 • The Passing Lane Observe the two cars below. The blue car starts

• The Passing Lane Observe the two cars below. The blue car starts "ahead of" the red car (which actually starts "off the screen"). Since the red car is moving faster, it eventually catches up with and passes the blue car. Observe the velocity-time graphs for these two cars. Each car's motion is represented by a horizontal line, indicating a constant velocity. Observe that even though the cars pass each other, the lines on the velocity-time graphs do not intersect. Since the cars never have the same velocity, the lines on the velocity-time graph never cross. The lines would intersect for a position vs. time graph; the fact that the red car passes the blue car means that there is an instant in which they occupy the same position. The two cars have the same position at seven seconds; yet they never have the same velocity at any instant in time.

Negative Velocity and Negative Acceleration • Observe that the object below moves in the

Negative Velocity and Negative Acceleration • Observe that the object below moves in the negative direction with a changing velocity. An object which moves in the negative direction has a negative velocity. If the object is speeding up then its acceleration vector is directed in the same direction as its motion (in this case, a negative acceleration). The "ticker tape" shows that each consecutive dot is not the same distance apart (i. e. , a changing velocity). The position-time graph shows that the slope is changing (meaning a changing velocity) and negative (meaning a negative velocity). The velocity-time graph shows a line with a negative (downward) slope (meaning that there is a negative acceleration); the line is located in the negative region of the graph (corresponding to a negative velocity). The acceleration-time graph shows a horizontal line in the negative region of the graph (meaning a negative acceleration).

Constant Positve Velocity • Observe that the object below moves with a constant velocity

Constant Positve Velocity • Observe that the object below moves with a constant velocity in the positive direction. The "ticker tape" shows that each consecutive dot is the same distance apart (i. e. , a constant velocity). The position-time graph shows that the slope is both constant (meaning a constant velocity) and positive (meaning a positive velocity). The velocity-time graph shows a horizontal line with zero slope (meaning that there is zero acceleration); the line is located in the positive region of the graph (corresponding to a positive velocity). The acceleration-time graph shows a horizontal line at the zero mark (meaning zero acceleration).

Direction of Acceleration and Velocity • Consider the motion of a Hot Wheels car

Direction of Acceleration and Velocity • Consider the motion of a Hot Wheels car down an incline, across a level, straight section of track, around a 180 -degree curve, and finally along a final straight section of track. Such a motion is depicted in the animation below. The car gains speed while moving down the incline - that is, it accelerates. Along the straight sections of track, the car slows down slightly (due to air resistance forces); again the car could be described as having an acceleration (or perhaps you prefer deceleration). Finally, along the 180 -degree curve, the car is changing its direction; once more the car is said to have an acceleration due to the change in the direction. Accelerating objects have a changing velocity - either due to a speed change (speeding up or slowing down) or a direction change.

Acceleration • Observe the animation of the three cars below. Which car or cars

Acceleration • Observe the animation of the three cars below. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. If necessary, review the definition of acceleration. As a final test of your understanding, consider the position-time graph at the right. Each one of the three lines on the position-time graph corresponds to the motion of one of the three cars. Match the appropriate line to the particular color of car.

Negative Velocity and Positive Acceleration • Observe that the object below moves in the

Negative Velocity and Positive Acceleration • Observe that the object below moves in the negative direction with a changing velocity. An object which moves in the negative direction has a negative velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a positive acceleration). The "ticker tape" shows that each consecutive dot is not the same distance apart (i. e. , a changing velocity). The position-time graph shows that the slope is changing (meaning a changing velocity) and negative (meaning a negative velocity). The velocity-time graph shows a line with a positive (upward) slope (meaning that there is a positive acceleration); the line is located in the negative region of the graph (corresponding to a negative velocity). The acceleration-time graph shows a horizontal line in the positive region of the graph (meaning a positive acceleration).

Positive Velocity and Negative Acceleration • Observe that the object below moves in the

Positive Velocity and Negative Acceleration • Observe that the object below moves in the positive direction with a changing velocity. An object which moves in the positive direction has a positive velocity. If the object is slowing down then its acceleration vector is directed in the opposite direction as its motion (in this case, a negative acceleration). The "ticker tape" shows that each consecutive dot is not the same distance apart (i. e. , a changing velocity). The position-time graph shows that the slope is changing (meaning a changing velocity) and positive (meaning a positive velocity). The velocity-time graph shows a line with a negative (downward) slope (meaning that there is a negative acceleration); the line is located in the positive region of the graph (corresponding to a positive velocity). The acceleration-time graph shows a horizontal line in the negative region of the graph (meaning a negative acceleration).

Constant Negative Velocity • Observe that the object below moves with a constant velocity

Constant Negative Velocity • Observe that the object below moves with a constant velocity in the negative direction. The "ticker tape" shows that each consecutive dot is the same distance apart (i. e. , a constant velocity). The position-time graph shows that the slope is both constant (meaning a constant velocity) and negative (meaning a negative velocity). The velocity-time graph shows a horizontal line with zero slope (meaning that there is zero acceleration); the line is located in the negative region of the graph (corresponding to a negative velocity). The acceleration-time graph shows a horizontal line at the zero mark (meaning zero acceleration).

Two-Stage Rocket • Observe the motion of the two-stage rocket and the corresponding velocitytime

Two-Stage Rocket • Observe the motion of the two-stage rocket and the corresponding velocitytime graph below. The rocket has two consecutive fuel stages followed by a free-fall motion (no fuel). In the two fuel stages, the rocket experiences an upward acceleration of +10 m/s/s and +4. 29 m/s/s respectively. This acceleration is depicted by the slope on the velocity-time graph. After ten seconds, the second fuel stage ends and the rocket is acted upon only by the force of gravity. It subsequently experiences a downward acceleration of -10 m/s/s. Note however, that from 10 to 16 seconds, the rocket continues moving upward (the velocity values are positive). During these six seconds, the rocket is moving upward but slowing down (the acceleration is downwards or negative as denoted by the negativelysloped line). It is not until after t=16 seconds that the rocket begins to move downwards.