Average speed is the total distance traveled by an object divided by the time taken to travel that distance.
Instantaneous speed is an object’s speed at a given instant of time.
2-2. Vectors
The magnitude of a quantity tells how large the quantity is.
There are two types of quantities:
Scalar quantities have magnitude only
Vector quantities have both magnitude and direction
Velocity is a vector quantity that includes both speed and direction.
A vector can be represented by an arrowhead line whose length is proportional to the magnitude of some quantity and whose direction is that of the quantity.
2-3. Acceleration
The acceleration of an object is the rate of change of its velocity and is a vector quantity.
For straight-line motion, average acceleration is the rate of change of speed:
where a = acceleration, t = time, vf = final speed, and vi = initial speed.
2-4. Distance, Time, and Acceleration
Speed and acceleration are defined quantities.
Relating speed and acceleration to each other and to time (a measurable quantity) allows the formation of equations that can answer certain questions involving distance, time, and acceleration.
2-5. Free Fall
The acceleration of gravity (g) for objects in free fall at the earth’s surface is 9.8 m/s2.
An object thrown horizontally has a vertical acceleration of 9.8 m/s2 and a constant horizontal velocity; its trajectory is a curved path.
An object thrown upward falls back to earth at an acceleration of 9.8 m/s2 and returns to its starting point with the same speed at which it was thrown.
An object thrown downward has a final speed that is the sum of its original speed plus the increase in speed due to the acceleration of gravity.
An object thrown upward at an angle to the ground follows a curved path called a parabola.
2-6. Air Resistance
Air resistance prevents a falling object from reaching the full speed produced by the acceleration of gravity.
Air resistance increases with the speed of a moving object.
Terminal speed is the maximum speed a falling object obtains when the force due to downward acceleration of gravity is balanced by the upward force of air resistance.
The terminal speed for any object depends on the object’s size, shape, and mass.
2-7. First Law of Motion
Isaac Newton formulated the three laws of motion.
The first law of motion states: If no net force acts on it, an object at rest remains at rest and an object in motion remains in motion at a constant velocity.
A force is any influence that can cause an object to be accelerated.
Every acceleration can be traced to the action of a force.
2-8. Mass
Inertia is the apparent resistance an object offers to any change in its state of rest or motion.
The mass of a body is the property of matter that manifests itself as inertia.
Mass may be thought of as a quantity of matter.
The greater an object’s mass, the greater the object’s inertia.
The SI unit for mass is the kilogram (kg).
2-9. Second Law of Motion
Newton’s second law of motion states: The net force on an object equals the product of the mass and the acceleration of the object. The direction of the force is the same as that of the acceleration.
The second law of motion can be expressed in either of these ways:
The pound (lb) is the unit of force in the British system of measurement:
1 lb = 4.45 N (1 N = 0.225 lb)
2-10. Mass and Weight
The weight of an object is the force with which gravity pulls it toward the earth:
w = mg
where w = weight, m = mass, and g = acceleration of gravity (9.8 m/s2).
In the SI, mass rather than weight is normally specified.
On earth, the weight of an object (but not its mass) can vary because the pull of gravity is not the same everywhere on earth.
2-11. Third Law of Motion
The third law of motion states: When one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.
No force ever occurs singly; for every action force there is an equal but opposite reaction force:
The action force is the force the first object exerts on the second.
The reaction force is the force the second object exerts on the first.
2-12. Circular Motion
Centripetal force is the inward force exerted on an object to keep it moving in a curved path:
where Fc = centripetal force, m = mass, v = speed, and r = radius of circular path.
The greater the object’s mass, the greater the centripetal force.
The faster the object moves, the greater the centripetal force.
The smaller the circle (curved path) of the object, the greater the centripetal force.
Highway curves are banked so that the horizontal component of the reaction force the tilted road exerts on the car provides the centripetal force needed to keep the car from skidding.
2-13. Newton’s Law of Gravity
Newton used Galileo’s work on falling bodies and Kepler’s three laws of gravity to develop his law of gravity.
Newton’s law of gravity states: Every object in the universe attracts every other object with a force proportional to both of their masses and inversely proportional to the square of the distance between them.
where F = force, G = gravitational constant (6.670 x 10—11 N · m2/kg2), and m1 = mass of object 1, m2 = mass of object 2, and R = distance between objects.
The force of gravitation drops off rapidly as the distance between two objects increases.
The center of mass of an object is the point where the mass of the object appears to be concentrated; for a uniform sphere the center of mass is its geometric center.
2-14. Artificial Satellites
The world’s first artificial satellite was Sputnik I, launched in 1957 by the Soviet Union.
A satellite in a geostationary orbit remains in place indefinitely over a particular location on the earth.
To maintain a circular orbit, the centripetal force on the satellite must be equal to the gravitational force on the satellite.
The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h.
