Download a = Vf - Vi t a = 2d t a = F m

Name ____________________________________________________________ Hour___________
Speed, Velocity and Acceleration…look how far we have come!
1. Define speed (Not just the formula!):
The rate at which an object covers a distance.
2. Define velocity (It’s not just speed!):
The rate at which an object changes position; speed in a given direction.
3. Define acceleration:
The rate at which an object’s velocity changes.
4. Explain how it is possible two different objects to have identical velocities.
Both would be traveling the same speed in the same direction.
5. Is it possible for a Hummer and a Smart car to have the same velocity? Explain.
Yes, regardless of mass both objects could have the same velocity.
6. Describe two situations in which a person or a vehicle maintains constant speed while
accelerating?
1) A car that changes lanes on the highway. 2) an ice skater doing a “figure 8”
7. As the moon revolves around the Earth on its monthly trip, it is always accelerating. How is this
possible?
It is constantly changing directions as it orbits the Earth.
8. Explain how it is possible for two different cars to be traveling along highway 70 at the same
speed but have different velocities.
The two cars can be traveling at the same speed but in different directions.
Behold the magical formulas that will help us to calculate the acceleration of an object
under most circumstances:
a = Vf - Vi
t
The acceleration of an object is equal to the final velocity minus the
initial velocity divided by the time it takes to change velocity.
a = 2d
t2
The acceleration of an object is equal to two times the distance
traveled divided by the square of the time it takes to travel the
distance.
a = F
m
You know this equation as Newton’s 2nd Law: The acceleration of an
object is equal to the force causing the acceleration divided by the
mass of the object.
___________________________________________________________________________
Use your own paper to perform these calculations:
a. Write out the complete formula first. Short cuts will not be awarded points.
b. Enter all of the information provided by the word problem into the formula with the appropriate
units of measurement. Failure to do this is a short cut.
c. Circle your final answer with the proper final unit of measurement. No short cuts.
d. Please round off all calculations to the nearest .01
1.
A Mercedes 500 class speeds up from rest to 100
km
/hr
in
4 seconds.
What is the car’s acceleration?
a = Vf - Vi
=
t
100 km/hr - 0km/hr
_______________________
2.
_______________________
4s
The same Mercedes speeds up from 100
=
100 km/hr
____________________
4s
= 25 km/hr /s
km
/hr to 200 km/hr in 10 seconds.
What is the car’s new acceleration?
a = Vf - Vi
=
t
200 km/hr - 100km/hr
_______________________
3.
_______________________
10 s
Usain Bolt’s world record for the 100
=
100 km/hr
=
_______________________
10 s
10 km/hr /s
m dash is 9.58 seconds.
What is his acceleration?
2 ( 100 m)
a = 2d
= (9.58 s)2
2
t
=
200 m
91.7764 s2
=
2.18 m/s2
4.
A train is accelerating at a rate of 2.0
km/hr/s.
what is its final velocity after 30 seconds?
a = Vf - Vi
t
=
5.
km/hr,
Vf = at + Vi
_______________________
Vf = at + Vi
If its initial velocity is 20
(2.0 km/hr/s)(30 s) + 20 km/hr
If a Smart car traveling at 60
=
60 km/hr + 20 km/hr
= 80 km/hr
km/hr comes to a complete stop in 5
seconds, what is its acceleration?
a = V f - Vi
_______________________
=
0 km/hr - 60km/hr
_______________________
t
6.
=
5s
- 60km/hr
______________________
_
=
5s
A grandma is traveling through Schnucks on a motorized scooter at 2
-12 km/hr/s
m/s.
She has to slow way down to a velocity of 1
into the canned goods aisle.
m/s to avoid rolling over during a vicious turn
If it takes her 5 seconds to make this change in velocity,
what is her acceleration?
a = V f - Vi
_______________________
t
=
1 m/s - 2m/s
_______________________
5s
=
- 1m/s
______________________
_
5s
=
- 0.2 m/s2
7.
A car with a mass of 2000
kg accelerates at a rate of 2 m/s2.
What is the net force in Newtons that is causing this acceleration?
a=F
m
F
= ma
= (2000 kg )(2 m/s2)
=
4000 N
Where did this unit come from?
1 Newton is (by definition) the amount of force needed to
accelerate one kilogram at a rate of 1 meter per second.
8.
An F-14 catapults off the flight deck of an aircraft carrier starting from
rest to a final
velocity of 68.2 m/s in just 2 seconds. If the mass of the jet is 29,545 kg, what
is the net force from the catapult that gets the jet into the air? (This is a 2 part problem)
Part 1
a = Vf - Vi
68.2 m/s - 0 m/s
=
t
2s
_______________________
_________________________________________________
=
34.1 m/s2
Part 2
a=F
m
F = ma = (29545 kg )(34.1 m/s2) = 1,007,484.50 N
9.
A Ferrari can accelerate from
rest to a velocity of 100 km/hr in 2.5 seconds.
If the Ferrari’s engine exerts a total net force of 4106 Newtons, what is the mass of the
car? (This is another 2 part problem)
a = Vf - Vi
100 km/hr - 0km/hr 100 km/hr
=
=
=
t
2.5 s
2.5 s
_______________________
______________________________________________
In order to use the next formula you’ll need to convert
40 km X 1000 m
1 hr
a=F
m
X
1 km
m =
F
a
1 hr
X
_______________________
40 km/hr /s
km
1 min
60 min
60 sec
=
4106 N
11.11 m/s2
/hr into m/s and then substitute it back.
=
11.11 m/s
= 369.5 kg
How did we get that unit?
If 1 N =
1kg · m
s2
2
then
1 kg =
N·s
--------------
m
N
=
--------------
m 2
/s
s2 = 1
1 2
/s
10. A wooden crate, holding an unknown, formerly living thing, is pushed quickly across an icy
2
backyard towards a shallow grave. If the crate’s acceleration is 0.08 m/s and its mass is
587.5 kg, what is the net force acting on the crate?
a=F
m
F = ma = (587.5 kg )(0.08 m/s2) = 47 N
11.
Three FHMS girls help an elderly man by pushing his stalled car out of an intersection. Each
2
girl pushes with a force of 400 Newtons. If the car accelerates at 0.85 m/s , what
is its mass?
a=F
m
12.
m=
F
=
a
If a giant boulder rolls 100
3 X 400 N
0.85 m/s2
=
1411.76 kg
m downhill towards a lodge filled with resting skiers in 10
seconds, what is its acceleration?
a = 2d
=
t2
13.
2 (100m)
10 s2
200 m
= 100 s2 =
2
m 2
/s
The road runner and Wyle E. coyote are running at the same velocity, 5
m/s. Realizing that
he might finally get caught, the roadrunner increases his velocity to 20 m/s in just
2 seconds. What is his rate of acceleration?
a = Vf - Vi
20 m/s - 5 m/s
15 m/s
=
=
=
t
2s
2s
_______________________
_________________________________
___________
7.5 m/s2
14.
A high powered projectile goes from
rest to 500 m/s in just 5 seconds.
What
is its acceleration?
a = Vf - Vi
500 m/s - 0 m/s
=
t
5s
_______________________
15.
___________________________________________
=
A Maserati is traveling along a super highway at 250
100 m/s2
km/hr.
The driver quickly hits the
brakes to avoid colliding with an elk in the middle of the road. If the Maserati comes to a
complete stop in 5 seconds, what is its acceleration?
a = Vf - Vi
0 km/hr - 250 km/hr
=
t
5s
_______________________
16.
_________________________________________________
-250 km/hr
=
= -50 km/hr/s
5s
________________________
A hungry barn owl is hunting for a juicy meal on a dark night. He is silently flying at an initial
velocity of 5
m/s when he spots a fat mouse in the field below.
of 15 m/s within 2 seconds, what is his acceleration?
a = Vf - Vi
15 m/s - 5 m/s
10 m/s
=
=
t
2s
2s
_______________________
_________________________________________
_____________
If he reaches a final velocity
= 5 m/s2
17. A parachute on the tail end of a racing dragster deploys and slows the velocity of the dragster
from 300
mi/hr to 50 mi/hr in 4 seconds.
What is the dragster’s acceleration?
a = Vf - Vi
50 mi/hr - 300mi/hr
-250 mi/hr
=
=
= -62.50 mi/hr/s
t
4s
4s
_______________________
_________________________________________________
_____________
18. If a man pushing a baby stroller (with a baby in it!) accelerates from 0
of 10
m/s to a final velocity
m/s in 5 seconds to outrun the police after robbing a bank so he could buy
some Pampers, what is his acceleration?
a = Vf - Vi
10 m/s - 0 m/s
=
t
5s
_______________________
19.
_______________________________________
A tennis ball with a mass of 0.314
=
2 m/s2
kg is accelerated at a rate of 162 m/s2 after a
professional player hits it. What is the net force exerted on the ball by the player’s racket?
a=F
m
F = ma = (0.314 kg)(162
m 2
/s )
=
50.87 N