Vectors represent physical quantities that involve both magnitude and direction, such as displacement, velocity, acceleration, force, electric and magnetic fields. A vector quantity is specified by both a magnitude and direction, while a scalar only involves magnitude and not direction. Examples of vector quantities include speed with a direction, such as 55 miles per hour to the north, as opposed to the scalar 55 miles per hour. The document then provides examples of calculating displacement, velocity, and acceleration for objects moving in various ways.
Vectors represent physical quantities that involve both magnitude and direction, such as displacement, velocity, acceleration, force, electric and magnetic fields. A vector quantity is specified by both a magnitude and direction, while a scalar only involves magnitude and not direction. Examples of vector quantities include speed with a direction, such as 55 miles per hour to the north, as opposed to the scalar 55 miles per hour. The document then provides examples of calculating displacement, velocity, and acceleration for objects moving in various ways.
Vectors represent physical quantities that involve both magnitude and direction, such as displacement, velocity, acceleration, force, electric and magnetic fields. A vector quantity is specified by both a magnitude and direction, while a scalar only involves magnitude and not direction. Examples of vector quantities include speed with a direction, such as 55 miles per hour to the north, as opposed to the scalar 55 miles per hour. The document then provides examples of calculating displacement, velocity, and acceleration for objects moving in various ways.
Vectors represent physical quantities that involve both magnitude and direction, such as displacement, velocity, acceleration, force, electric and magnetic fields. A vector quantity is specified by both a magnitude and direction, while a scalar only involves magnitude and not direction. Examples of vector quantities include speed with a direction, such as 55 miles per hour to the north, as opposed to the scalar 55 miles per hour. The document then provides examples of calculating displacement, velocity, and acceleration for objects moving in various ways.
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Vectors
• Vectors will show up all over the place in our
study of physics. Some physical quantities that are represented as vectors are displacement, velocity, acceleration, force, momentum, and electric and magnetic fields.
• A vector is a quantity that involves both
magnitude and direction. A quantity that does not involve direction is a scalar. For example, the quantity 55 miles per hour is a scalar, while the quantity 55 miles per hour to the north is a vector. KINEMATICS Example : A rock is thrown straight upward from the edge of a 30 m cliff, rising 10 m, and then falling all the way down to the base of the cliff. Find the rock’s displacement. Solution:
Displacement only refers to the object’s initial
position and final position, not the details of its journey. Since the rock started on the edge of the cliff and ended up on the ground 30 m below, its displacement is 30 m, downward. Its distance traveled is 50 m; 10 m on the way up and 40 m on the way down. Example:
An infant crawls 5 m east, then 3 m
north, and then 1 m east. Find the magnitude of the infant’s displacement. Example :
In a track-and-field event, an athlete runs
exactly once around an oval track, a total distance of 500 m. Find the runner’s displacement for the race. SPEED AND VELOCITY When we’re in a moving car, the speedometer tells us how fast we’re going; it gives us our speed. But what does it mean to have a speed of say, 10 m/s?
By definition, average speed is the ratio of the
total distance traveled to the time required to cover that distance: Example :
Assume that the runner completes the
500m oval in the race in 1 minute and 18 seconds. Find her average speed and the magnitude of her average velocity. Solution:
Average speed is total distance divided by
elapsed time. Since the length of the track is 500 m, the runner’s average speed was (500 m)/(78 s) = 6.4 m/s. However, since her displacement was zero, her average velocity was zero also: = Δx/Δt = (0 m)/(78 s) = 0 m/s. ACCELERATION Acceleration measures the rate of change of an object’s velocity. An object’s average acceleration is defined as follows: • Note that an object can accelerate even if its speed doesn’t change. (Again, it’s a matter of not allowing the everyday usage of the word accelerate to interfere with its technical, physics usage.)
•This is because acceleration depends on Δv, and the
velocity vector v changes if (1) speed changes, or (2) direction changes, or (3) both speed and direction change. • For instance, a car traveling around a circular racetrack is constantly accelerating even if the car’s speed is constant, because the direction of the car’s velocity vector is constantly changing. WEIGHT •Mass and weight are not the same thing there is a clear distinction between them in physics but they are often used interchangeably in everyday life.
•The weight of an object is the gravitational force
exerted on it by the Earth (or by whatever planet it happens to be on). Mass, by contrast, is a measure of the quantity of matter that comprises an object. weigh less on the Moon than you do on Earth. •An object’s mass does not change with location. Weight changes depending on location. For example, you weigh less on the Moon than you do on Earth.
•Since weight is a force, we can use F = ma to
compute it. What acceleration would the gravitational force impose on an object? The gravitational acceleration, of course! Therefore, setting a = g, the equation F = ma becomes