Speed, a.k.a. Velocity
by Dustin Glazier and Josh Patrice, January 1998
Table of Contents
New Quantities
X Displacement (meters: m)
t Time (seconds: s)
V Velocity (meters per second: m/s)
V_{a} Average Velocity (meters per second: m/s)
For our purposes we assume that V is constant and therefore the average Velocity
So on this page, V=V_{a}
These quantities are quite simplistic:
X represents the change in linear distance, or displacement;
For example, If you travel in a car for 120 meters, than X=120m
t is self explainitory, t= the amount of time taken for the change in X;
In the same car if it took you 1 minute, or 60 seconds, for X, then t=60s
V is the division of X and t, X/t, this is the speed;
The car with X=120m and t=60s, the velocity or speed = 2 m/s
Formulas
So now we have all the formulas we need for solving linear kinematics problems with
uniform velocity:

V = x/t

x = Vt

t = x/V
Go back to: Table of Contents
General Problem Solving Strategy:
 Read the problem.
 Go through the problem and figure out what is given or implied
Make a list, and identify the quantities you know.
 Find any formula that will allow you to calculate
anything that you don't know, and apply it.
 Add what you just found in the last step to your list of knowns.
 Check to see if you have found the answer. If not, repeat the
previous two steps until you are done.
Go back to: Table of Contents
Example problem 1
A cannon ball has a velocity of 32 m/s and it takes it 8 seconds to get out of the barrel.
Find the length of the barrel.
Here is what you start with:
X = ?
t = 8 seconds
V = 32 m/s
Dustin: So, if you look at the formulas, you can easily see the correct one to use.
Josh: Uhhhh, Dustin, they're all the same!!
Dustin: Oh yeah, but the one that solves for X looks real cool!
Josh: Oh yeah, good idea.
x = Vt
putting in numbers:
x= (32)(8)
so now you know the value of all the quantities:
X = 256 m
t = 8 sec
V = 32 m/s
So, other than the fact that this is ubsurd number,
we know the length of the cannon's barrel.
Go back to: Table of Contents
Example problem 2
A deranged and rabid squirrel scurries up a 50 meter tree in 2.5 seconds?
Find the velocity of this little fella.
Here's what we know:
X = 50 m
t = 2.5 sec
V = ?
Josh: So, if you look at the formulas, you can easily see the correct one to use.
Dustin: Uhhhh, Josh, they're all the same!!
Josh: Oh yeah, but the one that solves for V looks really cool!
Dustin: Oh yeah, good idea.
Let's use V = X/t
So, we then put the numbers in
V = (50)/(2.5)
Dustin: So we see that this squirrel can run at an olympic speed of 20 m/s.
Josh: Wow that's really fast!! Boy I tell you what I'd do if I had a squirrel that fast.
Dustin: No you won't.
Sample Problems
The answers to each problem follow it in parentheses. They also link to a solution to
the problem. Try the problem, check your answer, and go to the solution if you do not
understand.
1.
A car in front of the school goes 30.0 m in 2.35 seconds. What is its speed?
(12.8 m/s)
2.
What time will it take a car going 88 f/s to go 13 feet?
(.15 s)
3.
My Jetta can go 92 f in about 1.35 seconds. What is its speed?
(68 f/s)
4.
What is the speed of my Jetta from problem 3 in miles/hour? What is it's color?
(46 mph, Red)
5.
A glazier moves at a rate of 5.6 feet/day. What distance does he go in two weeks?
(78 f, Dustin's last name is Glazier, sounds like glacier)
Go back to: Table of Contents
6.
A trucker goes 345 miles in 7.0 hours. What is her speed?
(49 mph)
7.
A space shuttle moves at 3.4 miles/second. What distance does it go in one hour? How many feet?
(12240 mi, 6.5 x 10^{7} f)
8.
A car moving 44 feet/second takes what time to travel 16 feet?
(.36 s)
9.
What speed must you average to go 280 km in 3.0 hours?
(93 km/h)
10.
A river current moves at 3.2 miles/hour. How many seconds will it take you to drift 45 feet? (Convert to feet/second first)
(9.6 s)
11.
Convert 45 miles/hour to Feet/second
(66 f/s)
12.
Convert 60 km/hour to m/s
(17 m/s)
13.
Convert 80 feet/second to m/s
(24 m/s)
14.
A car in front of the school travels 15 feet in .38 seconds. What is its speed in m/s?
(12 m/s)
15.
A satellite travels at 5.4 miles in 3.2 seconds. What is its speed in miles/hour?
(6075 mph)
Go back to: Table of Contents
Solutions to Sample Problems
1.
A car in front of the school goes 30.0 m in 2.35 seconds. What is its speed?
( 12.8 m/s)
Here is what you start with:
 X = 30 m
 t = 2.35 sec
 V = ?
Try to put those numbers into formulas
V = (30 m)/ (2.35 sec)
We quickly find that V = 12.8 m/s
Josh: Just another useless tedious task setup by the schools to suck away our lives.
Dustin: Yeah, but in a fun way!
Go to: Problem Formulas Table of Contents
2.
What time will it take a car going 88 f/s to go 13 feet?
(.15s)
Here is what you start with:
 X = 13 ft
 t = ?
 V = 88 f/s
Plug those parts in and see what we get.
t = (13 ft)/(88 f/s)
t = .147727 or .15 seconds
Go to: Problem Formulas Table of Contents
3.
My Jetta can go 92 f in about 1.35 seconds. What is its speed?
(68 ft/sec)
Here is what you start with:
 X = 92 ft
 t = 1.35 seconds
 V = ?
I'm going to go out on a limb and say "try putting it in a formula"
V = (92 ft)/(1.35 sec)
V = 68 ft/sec
Dustin: You know Josh, it's a very nice Jetta.
Josh: Aww, well I wanted an M1 Abrahms tank, but the
dealership was all out, so I settled for it.
Go to: Problem Formulas Table of Contents
4.
What is the speed of my Jetta from problem 3 in miles/hour? What is it's color?
(46 mph, Red)
Here is what you start with:
 X = 92 ft
 t = 3.2 seconds
 V = 68 ft/sec
This is just conversion.
As we already know, there are 3600 seconds in an hour and 5280 feet in a mile
so we then multiply 68 by 3600
so 68 feet x 3600 sec
 
1 sec 1 hour
the seconds cancel out leaving feet per hour
and then divide by 5280
so 244800 feet x 1 mile
 
1 hour 5280 feet
This gives you miles per hour
And V = 46 mph
Josh: Listen, I was the first person at school with a Red Jetta and it's red because I like it.
Dustin: Yeah cause it makes it look like a Raisin!
Josh: A WHAT!
Dustin: A reallllyyyy cool Raisin?
Josh: Dustin, Raisin's aren't red!
Dustin: Yeah, but if they were, your car could look like one!
Go to: Problem Formulas Table of Contents
5.
A glazier moves at a rate of 5.6 feet/day. What distance does he go in two weeks?
()
Here is what you start with:
 X = ?
 t = 2 weeks or 14 days
 V = 5.6 feet/day
PUT THE NUMBERS IN A FORMULA!!!!
X = (14 days)(5.6 ft/days)
X = 78.4 feet
Josh: Do you really move that little?
Dustin: No, not always!
Josh: I should hope not.
Dustin: Sometimes less if I'm close to the refrigerator.
Go to: Problem Formulas Table of Contents
6.
A trucker goes 345 miles in 7.0 hours. What is her speed?
( 49 mph)
Here is what you start with:
 X = 345 miles
 t = 7 hours
 V = ?
Uhh, use those great formulas and work that physics magic
V = (345 miles)/ (7 hours)
Math yields the answer of 49 miles per hour or mph.
Go to: Problem Formulas Table of Contents
7.
A space shuttle moves at 3.4 miles/second. What distance does it go in one hour? How many feet?
(266 m)
Here is what you start with:
 X = ?
 t = 1 hr
 V = 3.4 miles/sec
We first break 1 hour down into seconds, there are 60 minutes in an hour and 60 seconds
therefore 3600 seconds in 1 hour.
Josh: And how many people wasting their time on this web page?
Dustin: Just us two, Josh.
Plug those parts in and see what we get.
X = (3600 sec)(3.4 miles/sec)
X = 12240 miles
However, Mr. Murray seems hell bent on using feet, so we must convert
Now, there are 5280 feet in a mile, so (12240 ft)(5280 ft/ mile)
And X = 64627200 feet or 6.5 x 10^{7}feet
Go to: Problem Formulas Table of Contents
8.
A car moving 44 feet/second takes what time to travel 16 feet?
(.36 s)
Here is what you start with:
 X = 16 ft
 t = ?
 V = 44 ft/s
Well let's find time:
Dustin: 10:45
Josh: No, moron. The time it takes to travel 16 feet!
Dustin: Oh, yeah.
V = X/t
(44) = (16)/t
t = (.36s)
Go to: Problem Formulas Table of Contents
9.
What speed must you average to go 280 km in 3.0 hours(93 km/h)
Here is what you start with:
 X = 280 km
 t = 3.0 hrs
 V = ?
Dustin: This problem is quite simple.
Josh: All the problems are quite simple.
Dustin: Uhh, yes but this one is even simpler!
V = (280)/(3.0)
V = (93 km/h)
Go to: Problem Formulas Table of Contents
10.
A river current moves at 3.2 miles/hour. How many seconds will it take you to drift 45 feet? (Convert to feet/second first)(9.6 s)
Here is what you start with:
 X = 45 ft
 t = ?
 V = 3.2 mi/h
First, let's convert the velocity to feet/seconds.
As we learned before,
so 3.2 miles x 1 hour
 
1 hour 3600 sec
the hours cancel out leaving miles per second
and then divide by 5280
so 3.2 miles x 5280 feet
 
3600 sec 1 mile
This gives you feet per second
And V = 4.69 ft/sec
t = (45)/(4.69)
t = (9.6s)
Go to: Problem Formulas Table of Contents
11.
Convert 45 miles/hour to Feet/second? (66 f/s)
If this has begun to look familiar to you, you're not alone
so 45 miles x 1 hour
 
1 hour 3600 sec
the hours cancel out leaving miles per second
and then divide by 5280
so 45 miles x 5280 feet
 
3600 sec 1 mile
This gives you feet per second
(66 f/s)
Josh: Boy I wish I had that tank.
Dustin: You are a small, small man. And you have my pity, farewell.
Go to: Problem Formulas Table of Contents
12.
Convert 60 km/hour to m/s? (17 m/s)
Boy oh boy another conversion problem!
all right 60 kilos x 1 hour
 
1 hour 3600 sec
this gives us km/sec
so 60 kilos x 1000 meters
 
3600 sec 1 kilo
thus giving us m/s.
In fact this gives us (17m/s).
Josh: Dustin?! Dustin?! Where have you gone? I feel so alone.
Go to: Problem Formulas Table of Contents
13.
Convert 80 feet/second to m/s?(24 m/s)
Josh: Dustin?
Dustin: Yes.
Josh: Where have you been?
Dustin: That is none of your concern little boy. And I'll thank you to stay out of my personal affairs.
Josh: How do we do this problem?
Dustin: The kids should just use their magical powers to make it wind up to be 24m/s.
Josh: Well, you heard the man.
Go to: Formulas Table of Contents
Problem Formulas Table of Contents