 # Linear Motion Test Review NOTES LOOK IT UP IN YOUR

```Linear Motion Test Review
1. What is the slope of the graph of position versus time? LOOK IT UP IN YOUR
NOTES
2. What is the slope of the graph of velocity versus time? LOOK IT UP IN YOUR
NOTES
3. Name three ways to accelerate. LOOK IT UP ON YOUR 2.3 GUIDED READING
4. What does it mean when the sign of the acceleration is different than the sign of the
velocity? Object is slowing down.
5. What does it mean when the sign of the acceleration is the same as the sign of the
velocity? Object is speeding up.
6. What is the difference in instantaneous and average acceleration? Look it up in your
7. What does the mathematical symbol lim represent? What does this mean? Lim
stands for limit. It means the value of an expression as some part of it
approaches a certain value.
8. What is the acceleration due to gravity? LOOK IT UP IN YOUR NOTES
9. An object is thrown in the air. Describe the object’s velocity and acceleration on the
way up, at the top, and on the way down? LOOK AT YOUR FREE FALL
PATTERNS EXERCISE
10. Which kinematic equation requires you to use the quadratic formula to solve for
time? 3rd
11. What are the underlying assumptions of the kinematics equations? Linear motion
& constant acceleration.
12. How does the velocity of an object thrown straight up compare to the velocity at the
same elevation on its way back down? LOOK AT YOUR FREE FALL
PATTERNS EXERCISE
13. How does the speed of an object thrown straight up compare to the speed at the same
elevation on its way back down? LOOK AT YOUR FREE FALL PATTERNS
EXERCISE
14. What do each of the three numbers mean that are computed in a linear regression
analysis? Slope, y-intercept, correlation coefficient
15. In a drag race, a dragster reaches the quarter mile (402 m) maker with a speed of 80
m/s. What is his acceleration and how long did the run take.
x f = 402m,x i = 0,v f = 80m / s,vi = 0
v 2f = v2i + 2a(x f − x i )
a=
v 2f − vi2
v2
(80m / s)2
= f =
= 7.96m / s 2
2(x f − x i ) 2x f
2(402m)
t=
v f − vi
80m / s
=
= 10.05s
2
a
7.96m / s
16. A body is released from rest and falls freely. Compute its position and velocity after
1,2,3, and 4 seconds. Take the origin 0 at the elevation of the starting point, and the
upward direction as positive.
v f = vi + at = 0 + (−9.8m / s 2 )t
v f = (−9.8m / s2 )t
1 2
2 2
at = 0 + 0 + .5(−9.8m / s )t
2
x f = (−4.9m / s 2 )t 2
x f = x i + vi t +
t(sec)
0
1
2
3
4
vf(m/s)
0
-9.8
-19.6
-29.4
-39.2
xf(m)
0
-4.9
-19.6
-44.1
-78.4
17. A ball is thrown upward with an initial speed of 80 ft./sec.
a) How high does it go?
b) What is its speed at the end of 3.0 seconds?
c) How high is it at that time?
2
vi = 80 ft / s,a = −32 ft / s
a)
v 2f = v2i + 2a(x f − x i )
vi2 = −2ax f
xf =
−vi2
−(80 ft / s) 2
=
2 = 100 ft.
2a 2(−32 ft / s )
b)
2
v f = vi + at = 80 ft / s − (32 ft / s )(3s) = −16 ft / s
c)
x f = x i + vi t +
1 2
1
at = (80 ft / s)(3s) − (32 ft / s2 )(3s)2 = 96 ft
2
2
18. Find an equation for the best line through the points below using linear regression.
x
y
1
3.05
2
5.1
3
6.98
4
8.99
5
12.0
y=(2.179)x+0.687 You must know how to do this on a TI-83 or TI-84.
19. Find an equation for the best line through the points below using linear regression
y
x
2
7.85
4
13.5
6
20.0
8
25.95
10
31.75
y=(3.0125)x+1.735 You must know how to do this on a TI-83 or TI-84.
20. A speed boat increases its speed from 50 ft/s to 80 ft/s in a distance of 200 ft. Find
the magnitude of its acceleration and the time it takes the boat to travel this distance.
x f = 200 ft,x i = 0,v f = 80 ft / s,vi = 50 ft / s
a)
v 2f = v2i + 2a(x f − x i )
a=
v 2f − vi2
2x f
2
2
=
(80 ft / s) − (50 ft / s)
= 9.75 ft / s 2
2(200 ft )
=
80 ft / s − 50 ft / s
= 3.08s
9.75 ft / s 2
b)
t=
v f − vi
a
21. The acceleration of gravity on the moon is about one sixth as great as on the earth. A
stone is thrown vertically upward on the moon, with an initial speed of 20 m/s. How
long will the stone remain in motion? What is the maximum height reached by the
stone relative to the moon's surface?
vi = 20m / s,v f = vtop = 0
a=
1
(−9.8m / s 2 ) = −1.63m / s 2
6
a)
v f − vi
0 − 20m / s
=
= 12.3s
a
−1.63m / s2
= 2xtup = 2 *12.3s = 24.6s
tup =
ttotal
b)
x f = x i + vi t +
1 2
1
at = (20m / s)(12.3s) + (−1.63m / s 2 )(12.3s )2 = 123m
2
2
22. A proton has an initial velocity of 2.5 x105 m/s and undergoes a uniform deceleration
of 5.0 x 1010 m/s2. What is its velocity after moving through a distance of 10 cm?
vi = 2.5x105 m / s, a = −5x1010 m / s 2 , x f = 10cm, xi = 0
v 2f = v2i + 2a(x f − x i ) = (2.5x10 5 m / s) 2 + 2(−5x1010 m / s 2 )(0.1m)
v f = 2.3x105 m / s
23. A bullet is fired through a board, 10 cm thick, in such a way that the bullet's line of
motion is perpendicular to the face of the board. If the initial speed of the bullet is
400 m/s and it emerges from the other side of the board with a speed of 300 m/s, find
the deceleration of the bullet as it passes through the board and the total time the
bullet is in contact with the board.
vi = 400m / s,v f = 300m / s, x f = 0.1m, xi = 0
a)
2
2
v f = vi + 2a(x f − x i )
2
2
v f − vi
a=
2x f
=
(300m / s)2 − (400m / s)2 = −350,000m / s2
2(0.1m)
b)
t=
v f − vi
a
=
(300m / s) − (400m / s)
−350,000m / s
2
= 2.86x10 −4 s
24. A go cart travels the first half of a 100 m track with a constant speed of 5 m/s. In the
second half of the track, it experiences a mechanical problem and decelerates at 0.2
m/s2. How long does it take the go-cart to travel the 100 m distance.
1)∆x = 50 m , v = 5m / s, a = 0
∆x
50 m
t=
=
= 10 s
v
5m / s
2) v i = 5m / s, ∆ x = 50 m , a = − 0.2m / s 2
1 2
at
2
50 m = (5m / s )t + .5( −0.2 m / s 2 )t 2
x f = x i + vi t +
t = 13.82sec (ignore second time,
t total = 10 s + 14 s = 24 s
its another lap)
25. The position time graph of a particle moving along the x axis is shown below.
Determine whether the velocity is positive, negative, or zero for the times t1, t2, t3,
and t4.
t1>0
t2=0
t3<0
t4=0
26. The velocity time graph for an object moving along the x axis is shown below. Plot a
graph of the acceleration versus time.
v(m/s)
a(m/s2)
t(s)
t(s)
27. Based on the following information, determine if the object is speeding up, slowing
down, moving to the right or moving to the left.
Velocity Sign
Acceleration Sign
+
+
-
+
+
Direction
Speeding Up or
Slowing Down
To complete this question, refer to your answer to numbers 1-2 & 4-5.
``` # 2.1a Uniform Motion Grahps.notebook October 12, 2014 v =   d # Velocity Acceleration Program 2015 - Hanson School District 30-1 # 1.) A ball is thrown straight down from the... of -22 feet per second. # Speed, Velocity and Acceleration Calculations Worksheet Part 1 