Motion Graphs, Measurement And Equations

Distance is a scalar quantity because it only has magnitude and no direction. Scalar quantities are described by their magnitude alone, while vector quantities, such as velocity and acceleration, have both magnitude and direction. Displacement is also a vector quantity because it represents the change in position and includes both magnitude and direction. Therefore, the correct answer is distance.

The position-time graph shows that the line representing object A has a steeper slope than the line representing object B. This indicates that object A is covering a greater distance in a shorter amount of time, which means it has a greater speed compared to object B.

The correct answer is B because a ball thrown vertically upward will experience a constant acceleration due to gravity, causing it to slow down and eventually stop at its highest point before falling back down. This motion is represented by a graph that starts at a positive position, reaches a maximum height, and then returns to the same position. Answer B shows this pattern accurately.

Displacement refers to the change in position of an object, which is zero if the object returns to its original position. In this case, since Jose Bautista runs around the bases and ends up back where he started, his displacement is zero. Average velocity is the displacement divided by the time taken, so if displacement is zero, average velocity would also be zero.

Since Kate and Michelle are running in opposite directions, they will have different velocities. Velocity is a vector quantity that includes both speed and direction. Even though they have the same constant speed, their directions are opposite, resulting in different velocities.

The object is travelling north, which means its velocity is in the north direction. However, it is slowing down, indicating that its acceleration is in the opposite direction of its velocity. Therefore, the directions associated with the object's velocity and acceleration are north (N) and south (S) respectively.

The area under an acceleration-time graph represents the change in velocity. This is because acceleration is the rate of change of velocity. By calculating the area under the graph, we can determine the total change in velocity over a specific time interval. The area can be positive or negative, indicating whether the velocity is increasing or decreasing. Therefore, the correct answer is "change in velocity."

The area under an acceleration-time graph does not give displacement. Displacement is determined by the area under a velocity-time graph. Acceleration is the rate of change of velocity, so the slope of a velocity-time graph gives acceleration. The slope of a position-time graph gives velocity, and the slope of the tangent in a position-time graph gives instantaneous velocity.

Graph D and E show acceleration because they both have a curved shape. In physics, acceleration is the rate at which an object changes its velocity over time. A curved graph indicates that the velocity of the object is changing, which is a characteristic of acceleration. Graphs A, B, and C do not show acceleration because they are either straight lines (indicating constant velocity) or horizontal lines (indicating no velocity change).

The acceleration-time graph in option D represents the ball's motion when thrown vertically upward into the air. This is because the graph shows a constant negative acceleration, which is the acceleration due to gravity acting on the ball as it moves against the direction of motion. The negative acceleration causes the ball to slow down until it reaches its highest point and then starts to fall back down.

The car drives 6.0 km east and then 8.0 km west, which means it covers a total distance of 14.0 km. The total time taken is 0.30 h. To find the average velocity, we divide the total distance by the total time. Therefore, the car's average velocity is 14.0 km / 0.30 h = 46.67 km/h. Since the car is traveling west, the velocity is negative. Converting km/h to m/s, we get 46.67 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 12.96 m/s. Rounding to the nearest meter, the car's average velocity is 13 m/s west, which is equivalent to 24 m/s west.

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The correct answer is that all three sections of the graph are comprised of horizontal lines. This is because the car reaches and maintains a constant velocity, which means there is no acceleration during that period. When the car slows down until it stops, it also experiences a uniform deceleration, which is represented by a horizontal line on the acceleration-time graph. Therefore, all three sections of the graph would show horizontal lines.