Chapter 2

• The space shuttle has released a parachute to reduce its speed quickly.
• The directions of the shuttle’s velocity and acceleration are shown by the green and gold arrows.
• Motion is described using the concepts of velocity and acceleration.
• In the case shown here, the velocity is to the right, in the direction of motion.
• The acceleration is in the opposite direction from the velocity which means the object is slowing down.
• We examine in detail motion with constant acceleration, including the vertical motion of objects falling under gravity.
• Two small heavy balls have the same diameter but one weighs twice as much as the other.
• The balls are dropped from a second-story balcony at the exact same time.
• The time to reach the ground below will be: twice as long for the lighter ball as for the heavier one.
• The change in x is calculated as
• The velocity of a car as a function of time is calculated as
• The average speed for the 200-km trip of a car is calculated as
• A car travels at a constant speed for 100 km, then speeds up to another constant speed and is driven another 100 km.
• The distance traveled by a cyclist in 2.5 hours is calculated as
• The runner’s average velocity is to the left, calculated as
• The average speed of a car is calculated as
• If you drive a car along a straight road for 150 km in 2.0 hours, the magnitude of your average velocity is
• Instantaneous velocity is the velocity at any instant of time, which is the magnitude of a speedometer reading.
• The motion of objects — baseballs, automobiles, joggers, and even the Sun and Moon — is an obvious part of everyday life.
• It was not until the sixteenth and seventeenth centuries that our modern understanding of motion was established.
• The slope of the line connecting the two points becomes closer and closer to the slope of a line tangent to the curve at point.
• Consider a time intermediate between and call it at which moment the object is at.
• The position of a falling object after a certain time can be calculated using the equation y = v0t + 1/2a t2.
• The instantaneous velocity equals the slope of the tangent to the curve of x v s at any chosen point, which can simply be called “the slope of the curve” at that point.
• Let us take point in Fig 2–28 to be closer and closer to point, making the time interval smaller and smaller.
• The slope of the line tangent to the curve at point equals the instantaneous velocity at time t1.
• The slope of the straight line is less than the slope of , thus the average velocity during the time interval is less than during the time interval t2 - t1.
• The definition of the instantaneous velocity (Eq 2–3) is the limiting value of the average velocity as approaches zero.
• The average velocity (equal to the slope of the chord) thus approaches the slope of the tangent at point.
• The speed of an object falling in air does not increase indefinitely, and if the object falls far enough, it will reach a maximum velocity called the terminal velocity due to air resistance.
• Acceleration due to gravity is a vector, with its direction being downward toward the center of the Earth.
• Air resistance will be noticeable even on a reasonably heavy object if the velocity becomes large.
• When dealing with freely falling objects, the equation for acceleration due to gravity can be simplified to: a = g = 9.80 m/s^2.
• The effects of air resistance are often small, and can be neglected for most purposes.
• The magnitude of acceleration due to gravity is approximately g = 9.80 m/s^2 on the Earth's surface.
• The motion of a falling object can be represented by the equation y = v0t + 1/2a t2, where v0 is the initial velocity and a is the acceleration.
• During the remaining portion of the race, Mary decelerates at a constant rate of to the finish line.
• In a foot race, when Mary is 22 m from the finish line, she has a speed of and is 5.0 m behind Sally, who has a speed of
• After the rocket runs out of fuel, its acceleration is that of gravity, downward.
• The best rebounders in basketball have a vertical leap of about 120 cm.