Motion. Measuring Motion. Speed Average Speed = distance covered / time taken v = d/t metric unit of speed: m/s English unit of speed: ft/s Constant speed: moving equal distances in equal time periods an object covering 5 feet each second has a constant speed of 5ft/s
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v = d/t
Constant speed:this car is moving in a straight line covering a distance of 1 mi each minute. The car, therefore, has a constant speed of 60 mi per each 60 min, or 60 mi/hr.
Velocity is a vector that we can represent graphically with arrows. Here are three different velocities represented by three different arrows. The length of each arrow is proportional to the speed and the arrowhead shows the direction of travel.
vf – vivi = initial velocity
t vf = final velocity
t = time interval
unit of velocity m/s
unit of time s
(A) This graph shows how the speed changes per unit of time while driving at a constant 30 mi/hr in a straight line. As you can see, the speed is constant, and for straight-line motion, the acceleration is 0.
(B) This graph shows the speed increasing to 50 mi/hr when moving in a straight line for 5 s. The acceleration is the slopeof the straight line graph of speed (on the y-axis) versus time (on the x-axis).
10 lb west
10 lb west
10 lb west
(A) This shows two equal forces (200 N each) acting at an angle of 90O, which give a resultant force (Fnet) of 280 N acting at 45O. (B) Two unequal forces acting at an angle of 60O give a single resultant of about 140 N.
(A) This ball is rolling to your left with no forces in the direction of motion. The vector sum of the force of floor friction (Ffloor) and the force of air friction (Fair) result in a net force opposing the motion, so the ball slows to a stop.
(B) A force is applied to the moving ball, perhaps by a hand that moves along with the ball. The force applied (Fapplied) equals the vector sum of the forces opposing the motion, so the ball continues to move with a constant velocity.
Thus, an object moving through space without any opposing friction (A) continues in a straight line path at a constant speed. The application of an unbalanced force as shown by the large arrow, is needed to (B) slow down, (C) speed up, or, (D) change the direction of travel.
Galileo (1564-1642)challenged the Aristotelian view of motion and focused attention on the concepts of distance, time, velocity, and acceleration
According to a widespread story, Galileo dropped two objects with differentweights from the Leaning Tower of Pisa. They were supposed to have hit the ground at about the same time, discrediting Aristotle's view that the speed during the fall is proportional to weight.
The actual leaning tower of Pisa taken by my friend Larry Heath, Emeritus Professor of Technology on his recent trip to Rome
v = d/ t
d = vt
(vi +vf) (t)
vf - vi
but vi = 0, which givesa = vf /t
Solve for vf :
vf = at
d = (1/2)at2 which gives the distance covered in the free fall
An object dropped from a tall building covers increasing distances with every successive second of falling. The distance covered is proportional to the square of the time falling (d t2).
On its way up, a vertical projectile such as a misdirected golf ball is slowed by the force of gravity until an instantaneous stop; then it accelerates back to the surface, just as another golf ball does when dropped from the same height. The straight up and down moving golf ball has been moved to the side in the sketch so we can see more clearly what is happening.
A horizontal projectile has a constant horizontal velocity and an increasing vertical velocity as it falls to the ground. The combined effect of the two velocities results in a curved path (parabola). Neglecting air resistance, an arrow shot horizontally will strike the ground at the same time as one dropped from the same height above the ground, as shown here by the increasing vertical velocity arrows.
Projectilethrownat an angleA football is thrown at some angle. Neglecting air resistance, the horizontal velocity is constant, and the vertical velocity decreases (on the way up) then increases (on the way down), just as in the case of a vertical projectile. The combined motion produces a parabolicpath.