Motion and Forces
Speed, Distance and Time
Speed: Speed refers to the rate at which an object moves (in other words, how fast it is moving). It can be measured with a variety of units, including m/s (meters per second) and km/h (kilometers per hour). Speed is represented by the symbol v.
Constant speed: An object is moving at a constant speed when its speed remains the same throughout the duration of its motion.
Distance: Distance is the length of the path that an object travels. It can be measured in km (kilometers), m (meters), mi (miles), yd (yards), etc. Distance is represented by the symbol d.
Time interval: Time interval refers to the amount of time that has passed between the starting and ending point of an object’s motion. It can be measured in s (seconds), min (minutes), h (hours), etc. Time interval is represented by
the symbol Δt.
The relationship between speed, distance and time is characterized by the equation
v = d
Δt
where v is measured in m/s, d is measured in m and Δt is measured in s.
If the speed of an object is not constant throughout the distance it travels, the previous equation is replaced by
vave = d
Δt
where vave represents constant speed and all the units from the previous equation remain the same.
Example 1: What is the speed of a ball that rolls 16m in 2s?
d = 16m
Δt = 2s
v = ?
v = d
Δt
v = 16m
2s
v = 8m
s
The ball is rolling at a speed of 8m/s.
Example 2: A cat running at 5m/s travels a distance of 15m before suddenly stopping. For how long did the cat
run?
v = 5m/s
d = 15m
Δt = ?
v = d
Δt
5m = 15m
s Δt
(5m)(Δt) = (15m)(1s)
Δt = (15m)(1s)
5m
Δt = 3s
The cat ran for 3s.
Example 3: A pedestrian walked for 30 minutes at a rate of 2m/s. How far did he travel?
Δt = 30 min × 60s/min = 1800s
v = 2m/s
d = ?
v = d
Δt
2m = d
s 1800s
(2m)(1800s) = d(1s)
(2m)(1800s) = d
s
3600m = d
He traveled 3600m.
Practice
http://www.airdrie.n-lanark.sch.uk/airmaths/Speed,%20Distance,%20Time%20Worksheet.pdf
http://mrsharmonscience.weebly.com/uploads/1/3/2/2/13222665/distance_time_speed.pdf
http://www.armyofficerselectionboard.co.uk/speed-distance-time/test
http://math.about.com/od/algebra1help/a/Solving-Problems-Involving-Distance-Speed-And-Time.htm
Labs
http://aspire.cosmic-ray.org/javalabs/java12/fnm/act1/lab.htm
http://sunshine.chpc.utah.edu/javalabs/java12/fnm/act1/tchrpage.htm (goes with previous page)
http://sciencespot.net/Media/speedchall.pdf
http://wp.lps.org/mtest/files/2012/08/Determing-speed-lab.pdf
Speed: Speed refers to the rate at which an object moves (in other words, how fast it is moving). It can be measured with a variety of units, including m/s (meters per second) and km/h (kilometers per hour). Speed is represented by the symbol v.
Constant speed: An object is moving at a constant speed when its speed remains the same throughout the duration of its motion.
Distance: Distance is the length of the path that an object travels. It can be measured in km (kilometers), m (meters), mi (miles), yd (yards), etc. Distance is represented by the symbol d.
Time interval: Time interval refers to the amount of time that has passed between the starting and ending point of an object’s motion. It can be measured in s (seconds), min (minutes), h (hours), etc. Time interval is represented by
the symbol Δt.
The relationship between speed, distance and time is characterized by the equation
v = d
Δt
where v is measured in m/s, d is measured in m and Δt is measured in s.
If the speed of an object is not constant throughout the distance it travels, the previous equation is replaced by
vave = d
Δt
where vave represents constant speed and all the units from the previous equation remain the same.
Example 1: What is the speed of a ball that rolls 16m in 2s?
d = 16m
Δt = 2s
v = ?
v = d
Δt
v = 16m
2s
v = 8m
s
The ball is rolling at a speed of 8m/s.
Example 2: A cat running at 5m/s travels a distance of 15m before suddenly stopping. For how long did the cat
run?
v = 5m/s
d = 15m
Δt = ?
v = d
Δt
5m = 15m
s Δt
(5m)(Δt) = (15m)(1s)
Δt = (15m)(1s)
5m
Δt = 3s
The cat ran for 3s.
Example 3: A pedestrian walked for 30 minutes at a rate of 2m/s. How far did he travel?
Δt = 30 min × 60s/min = 1800s
v = 2m/s
d = ?
v = d
Δt
2m = d
s 1800s
(2m)(1800s) = d(1s)
(2m)(1800s) = d
s
3600m = d
He traveled 3600m.
Practice
http://www.airdrie.n-lanark.sch.uk/airmaths/Speed,%20Distance,%20Time%20Worksheet.pdf
http://mrsharmonscience.weebly.com/uploads/1/3/2/2/13222665/distance_time_speed.pdf
http://www.armyofficerselectionboard.co.uk/speed-distance-time/test
http://math.about.com/od/algebra1help/a/Solving-Problems-Involving-Distance-Speed-And-Time.htm
Labs
http://aspire.cosmic-ray.org/javalabs/java12/fnm/act1/lab.htm
http://sunshine.chpc.utah.edu/javalabs/java12/fnm/act1/tchrpage.htm (goes with previous page)
http://sciencespot.net/Media/speedchall.pdf
http://wp.lps.org/mtest/files/2012/08/Determing-speed-lab.pdf
Force
Force is a push or pull that, when applied to an object, can alter the object’s motion or shape.
It is measured in Newtons (N) and is represented by the symbol F.
Some of the characteristics of force include:
-It can act either through direct contact (i.e. a push or pull) or at a distance (ex: gravitational force).
-In a diagram, it is represented by an arrow. The magnitude (size) of the force is indicated by the length of the arrow or by a number. The direction of the force is indicated by the direction the arrow is pointing in.
-The point of application of a force is the place where the force is applied.
Force is a push or pull that, when applied to an object, can alter the object’s motion or shape.
It is measured in Newtons (N) and is represented by the symbol F.
Some of the characteristics of force include:
-It can act either through direct contact (i.e. a push or pull) or at a distance (ex: gravitational force).
-In a diagram, it is represented by an arrow. The magnitude (size) of the force is indicated by the length of the arrow or by a number. The direction of the force is indicated by the direction the arrow is pointing in.
-The point of application of a force is the place where the force is applied.
Mass versus Weight
Mass is the amount of matter an object contains. It remains constant regardless of the conditions the object is subjected to (ex: gravity). Mass is represented by the symbol m and is usually measured in kg (kilograms) or g (grams).
Weight is the force as a result of gravity. It takes in account both the mass of an object and the gravitational acceleration. Weight is represented by the symbol Fg and is measured in N (newtons).
The gravitational acceleration on Earth is 9.8m/s2 (meters per second squared).
Mass, gravitational acceleration and weight can be related in the following formula:
Fg = mg
where Fg is measured in N, m is measured in kg and g is measured in N/kg or m/s2 (equivalent units).
Example 1: A book has a mass of 3kg. What is its weight?
m = 3kg
g = 9.8N/kg
Fg = ?
Fg= mg
= (3kg)(9.8N/kg)
= 29.4N
The weight of the book is 29.4N.
Example 2: On Planet X, the gravitational acceleration is 3.4m/s2. If an astronaut with a mass of 75kg were to visit this planet, what would his weight be?
g = 3.4m/s2 = 3.4N/kg
m = 75kg
Fg= ?
Fg= mg
= (75kg)(3.4N/kg)
= 255N
The astronaut’s weight would be 255N.
Practice
http://myhome.sunyocc.edu/~testones/MASSWEIGHT.rtf
http://www.nyu.edu/pages/mathmol/textbook/weightvmass.html
Mass is the amount of matter an object contains. It remains constant regardless of the conditions the object is subjected to (ex: gravity). Mass is represented by the symbol m and is usually measured in kg (kilograms) or g (grams).
Weight is the force as a result of gravity. It takes in account both the mass of an object and the gravitational acceleration. Weight is represented by the symbol Fg and is measured in N (newtons).
The gravitational acceleration on Earth is 9.8m/s2 (meters per second squared).
Mass, gravitational acceleration and weight can be related in the following formula:
Fg = mg
where Fg is measured in N, m is measured in kg and g is measured in N/kg or m/s2 (equivalent units).
Example 1: A book has a mass of 3kg. What is its weight?
m = 3kg
g = 9.8N/kg
Fg = ?
Fg= mg
= (3kg)(9.8N/kg)
= 29.4N
The weight of the book is 29.4N.
Example 2: On Planet X, the gravitational acceleration is 3.4m/s2. If an astronaut with a mass of 75kg were to visit this planet, what would his weight be?
g = 3.4m/s2 = 3.4N/kg
m = 75kg
Fg= ?
Fg= mg
= (75kg)(3.4N/kg)
= 255N
The astronaut’s weight would be 255N.
Practice
http://myhome.sunyocc.edu/~testones/MASSWEIGHT.rtf
http://www.nyu.edu/pages/mathmol/textbook/weightvmass.html
Frictional Force
The force of friction is the resistance that occurs when a moving object is in contact with a surface. It is represented by the symbol Ff. This force is dependent on the nature of the two materials in contact with each other, and also on the amount of contact force (the force pressing the two surfaces together).
Extra Notes
http://regentsprep.org/regents/physics/phys01/friction/default.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
The force of friction is the resistance that occurs when a moving object is in contact with a surface. It is represented by the symbol Ff. This force is dependent on the nature of the two materials in contact with each other, and also on the amount of contact force (the force pressing the two surfaces together).
Extra Notes
http://regentsprep.org/regents/physics/phys01/friction/default.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html
Equilibrium between Forces
When two or more forces are applied to an object and their net force (sum of forces) is 0, they are said to be in equilibrium. If this occurs while an object is at rest, it will continue to be at rest. However, if this occurs when an object is moving, it will continue to do so at a constant speed.
Extra Notes
http://www.physicsclassroom.com/class/vectors/u3l3c.cfm
When two or more forces are applied to an object and their net force (sum of forces) is 0, they are said to be in equilibrium. If this occurs while an object is at rest, it will continue to be at rest. However, if this occurs when an object is moving, it will continue to do so at a constant speed.
Extra Notes
http://www.physicsclassroom.com/class/vectors/u3l3c.cfm
Effective Force
A force can be split up into two components: one is vertical and the other is horizontal. The component that results in or changes the motion of an object is called the effective force. It is thus parallel to the displacement of the object.
A force can be split up into two components: one is vertical and the other is horizontal. The component that results in or changes the motion of an object is called the effective force. It is thus parallel to the displacement of the object.
Effective force and the force that is applied (F) are linked in the formula
Feff = F cos θ
where Feff and F are measured in N, and θ is the angle formed between the applied and effective forces.
Feff = F cos θ
where Feff and F are measured in N, and θ is the angle formed between the applied and effective forces.
Inclined Planes
When an object is placed on an inclined plane, the force of gravity acting on the object splits up into two components parallel (or horizontal) force (F∥) and perpendicular (or vertical) force (F⊥). These can be calculated using trigonometric principles.
Example: A box with a mass of 100kg is sitting on an inclined plane that is at a 30° angle. What are the values of the parallel and perpendicular forces?
When an object is placed on an inclined plane, the force of gravity acting on the object splits up into two components parallel (or horizontal) force (F∥) and perpendicular (or vertical) force (F⊥). These can be calculated using trigonometric principles.
Example: A box with a mass of 100kg is sitting on an inclined plane that is at a 30° angle. What are the values of the parallel and perpendicular forces?
Fg= mg
= (100kg)(9.8N/kg)
= 980N
F∥---> S = O
H
sin θ = O
H
(H)(sin θ) = O
(980N)(sin 30°) = O
490N = O
F⊥ ---> C = A
H
cos θ = A
H
(H)(cos θ) = A
(980N)(cos 30°) = A
848.7N = A
The parallel force is 490N. The perpendicular force is 848.7N.
This website provides a more detailed explanation about inclined planes and forces:
http://www.physicsclassroom.com/class/vectors/u3l3e.cfm
For an introduction or review of basic trigonometric principles, you can consult these links:
http://www.mathsisfun.com/algebra/sohcahtoa.html
http://www.mathwords.com/s/sohcahtoa.htm
SOH-CAH-TOA: Extra Notes and Practice
http://coachforrester.weebly.com/uploads/1/3/1/9/13191763/sohcahtoa_practice.pdf
http://www.algebralab.org/practice/practice.aspx?file=Trigonometry_SinCosTan.xml
http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent-practice2.php
= (100kg)(9.8N/kg)
= 980N
F∥---> S = O
H
sin θ = O
H
(H)(sin θ) = O
(980N)(sin 30°) = O
490N = O
F⊥ ---> C = A
H
cos θ = A
H
(H)(cos θ) = A
(980N)(cos 30°) = A
848.7N = A
The parallel force is 490N. The perpendicular force is 848.7N.
This website provides a more detailed explanation about inclined planes and forces:
http://www.physicsclassroom.com/class/vectors/u3l3e.cfm
For an introduction or review of basic trigonometric principles, you can consult these links:
http://www.mathsisfun.com/algebra/sohcahtoa.html
http://www.mathwords.com/s/sohcahtoa.htm
SOH-CAH-TOA: Extra Notes and Practice
http://coachforrester.weebly.com/uploads/1/3/1/9/13191763/sohcahtoa_practice.pdf
http://www.algebralab.org/practice/practice.aspx?file=Trigonometry_SinCosTan.xml
http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent-practice2.php
Powerpoints on Motion and Forces
http://science.pppst.com/motion.html
http://science.pppst.com/motion.html