Linear Acceleration
by Jason "Mussolini" Crandall and Joe "Stalin" Thaler, December 1997
1.
A car in front of the school goes from rest to 27 m/s
in 3.0 seconds. What is its acceleration? Here is what you start with:
Once again, our formula is:
V = V_{o} + at
Plug in the initial and final velocities and the time and calculate the acceleration.
27 m/s = 0 m/s + (a * 3.0 seconds)
Our solution is 9 m/s/s.
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2.
A train can speed up at a rate of .053 m/s/s. What time
will it take for it to reach a speed of 21 m/s from a standing stop?
Here is what you start with:

t = ?

V_{o} = 0 (assumed)

V = 21 m/s

a = .053 m/s/s
Once again, our formula is:
V = V_{o} + at
Thus:
21 m/s = 0 + (.053 m/s/s * t)
Solve for t and you get 396 seconds.
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3.
A rocket accelerates at a rate of 190 m/s/s for 2.4 seconds
from rest.
What is its final speed? (456 m/s)
Here is what you start with:

t =2.4 s

V_{o} = 0 (assumed)

V = ?

a = 190 m/s/s
You can use V = V_{o} + at to find the final velocity:
V = 0 + (190 m/s/s)(2.4 s) = 456 m/s
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4.
A car has a velocity of +15 m/s. It then accelerates at a
rate of +3.5 m/s/s for the next 5 seconds. What is its final velocity? What is your
favorite ice cream flavor (chocolate and vanilla do not apply)?
(32.5 m/s, pralines and cream)
Here is what you start with:
Use V = V_{o} + at to find the final Velocity:
V = 15 m/s + (3.5 m/s/s)(5 s) = 32.5 m/s
Now the ice cream part is a little bit more tricky. Without any formulas, we are forced to
rely upon empirical observation. Therefore I took it upon myself to sample all 31 flavors
at BaskinRobbins. One empty wallet and several ice cream headaches later, I have come to
the conclusion that Pralines and Cream is the favorite ice cream flavor. Judging from my
experience, attempts to reproduce this experiment may be hazardous to your health and
financial wellbeing.
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5.
A car involved in an 14 m/s collision with a parked car is
determined to have skidded for a time of 3.7 seconds before the impact. If that particular
car can brake at 8.2 m/s/s with the tires locked, how fast was the car going before it hit
its brakes?
(44 m/s)
Here is what you start with:
t = 3.7 s
V_{o} = ?
V = 14 m/s (at impact)
a = 8.2 m/s/s
Use V = V_{o} + at to find the initial Velocity:
14 m/s = V_{o} + (8.2 m/s/s * 3.7 s)
Thus (use a little algebra), V_{o} is 44 m/s. 44 m/s is approximately 98 mph, so our
little friend probably deserves whatever he gets.
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6.
A spaceship with a velocity of +320 m/s fires its retro
rockets to slow it at a rate of 22 m/s/s for 3 seconds. How fast is the rocket ship going
after that?
(254 m/s)
Here is what you start with:
t = 3 s
V_{o} = 320 m/s
V = ?
a = 22 m/s/s
Using V = V_{o} + at to find the final velocity:
V = 320 + (22 m/s/s * 3 s) = 254 m/s
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7.
What time will it take a car that can accelerate from 0 m/s
to 20 m/s in 5 seconds to speed up from 12 m/s to 27 m/s? (Find the acceleration)
(3.75 s)
Here we have two problems:
t = ?
V_{o} = 12 m/s
V = 27 m/s
a = ?
This is not yet solvable, because we don't know the acceleration.
Let's assume that the acceleration from 12 m/s to 27 m/s is the same
as it is from 0 to 20 m/s. In order to find
the acceleration we use our
favorite formula again: V = V_{o} + at.
20 m/s = 0 m/s + (a * 5 s) (Look at the first 3 numbers
and we get a = 4 m/s/s
We now know:

t = ?

V_{o} = 12 m/s

V = 27 m/s

a = 4 m/s/s
Now find the time using the our favorite formula once again: V = V_{o} + at.
27 m/s = 12 m/s + (4 m/s/s * t)
Thus, solving for t, we arrive at the answer: 3.75 seconds.
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8.
A baseball can change its velocity from +45 m/s to 52 m/s
in the .015 seconds that it takes to hit a line drive. What is the acceleration of the ball?
(6500 m/s/s Rounded)
Here is what you start with:

t = .015 s

V_{o} = +45 m/s

V = 52 m/s

a = ?
Find the acceleration using the our freindly neighborhood aceleration formula once again:
V = V_{o} + at.
Plug in a couple of numbers and get:
52 m/s = 45 m/s + (a * .015 s)
Solve for a, and we get approximately 6466.66 m/s/s, which, in case you didn't know, is
really, REALLY fast. Using sig figs, we get 6500 m/s/s.
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9.
What must be your acceleration if you change your velocity
from 34 m/s to 21 m/s in 15 seconds?
(.87 m/s/s)
Here is what you start with:

t = 15 s

V_{o} = 34 m/s

V = 21 m/s

a = ?
Okay boys and girs, let's see if we can possibly guess what formula we're going to use today.
What's that I hear you saying? Very good! It IS: V = V_{o} + at.
Let's go to the numbers:
21 m/s = 34 m/s + (a * 15 s)
After a random survey, the majority of people polled feel that .87 m/s/s is the correct answer.
However, 9% of our respondents DO NOT like Pralines and Cream.
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10.
Objects accelerate downwards at 32 f/s/s near the surface
of the earth. For how much time must you fall to reach 60 miles/hour? Convert! (2.75 s)
Here is what you start with:
Okay, I'm getting kind of tired of restating our favorite formula, so here it is with the
numbers already plugged in:
88 f/s = 0 + (32 f/s/s * t)
Me: I'll take acceleration for $500 Alex.
Alex: And the answer is, 88 f/s divided by 32 f/s/s.
Me: What is 2.75 seconds?
Alex: That's right! You win, now get off the web and go do something useful!
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