Full Name ______________________________
ACCELERATION PRACTICE PROBLEMS
Date ________ Period __________ Seat _____
Use the equations shown in the box to solve the following problems. Be sure to show your work
1. A roller coaster car rapidly picks up speed as it rolls down a
slope. As it starts down the slope, its speed is 4 m/s. But 3
seconds later, at the bottom of the slope, it speed is 22 m/s.
What is its average acceleration?
a =
2. At the bottom of the slope, the roller coaster is traveling 22 m/s.
As it starts up the next hill, gravity causes it to decelerate at a
rate of -6.0 m/s 2. After 3.5 seconds of climbing, it reaches the
top of the hill. What is its final velocity?
∆t =
vf – vo
∆t
vf – vo
a
vf = ( a ∙ ∆t ) + vo
vo = vf – ( a ∙ ∆t )
3. Barely crawling over the second hill at 1.0 m/s, the roller coaster
plunges down a very steep slope, accelerating at an average rate
of 8.0 m/s 2. At the bottom of the slope it attains a speed of 29 m/s
(equal to 65 mi/h). How long did it take for the roller coaster to
reach the bottom of the slope?
4. The roller coaster then enters a double loop. When it exits the last
loop, it begins decelerating at a constant rate of -3.0 m/s 2, which
takes 6.0 seconds to reach the unloading gates and come to a stop.
What was the coaster’s original velocity when it exited the loop?
1
Full Name ______________________________
ACCELERATION PRACTICE PROBLEMS
5.
Date ________ Period __________ Seat _____
Bob and Ted are having a bicycle race on straight track marked out in meters. Bob is a
6th grader, and Ted is a senior. Since Ted is older and stronger, he allows Bob to build up
speed before crossing the starting line.
When the race starts, Bob gets his bike up to a top speed of 3 m/s. Ted, starting at rest,
begins to peddle when Bob passes him. Ted accelerates at a constant 1.0 m/s 2 until he
reaches a top speed of 7 m/s.
1)
2)
3)
4)
5)
Use the formulas in the box to help you complete data tables A and B below.
Using graph 1, plot distance vs time for both Bob and Ted.
Using graph 2, plot speed vs time for both Bob and Ted.
Include a legend for each graph, so that Bob’s data can be discerned from Ted’s.
For each graph, draw a trend line through the data points.
Study the two graphs you made, then answer the following questions:
1) At what distance did Ted finally overtake Bob?
Use this formula for table A
d = v ∙ ∆t
2) How long into the race did Ted finally overtake Bob?
Use these formulas for table B
at2
∆d =
2
3) How fast was Ted going when he finally caught Bob?
vf = ( a ∙ ∆t ) + vo
4) At what point in time did Ted reach his top speed of 7 m/s?
A
B
Ted (Acceleration = 1.0 m/s2)
Time
Distance
Velocity
(s)
(m)
(m/s)
0
0
0
1
2
3
4
5
6
7
Bob (Constant speed = 3 m/s)
Time
Distance
Velocity
(s)
(m)
(m/s)
0
0
3
1
2
3
4
5
6
7
2
Full Name ______________________________
ACCELERATION PRACTICE PROBLEMS
Date ________ Period __________ Seat _____
Graph 1
Distance as a Function of Time (Speed Graph)
26
Legend
24
Bob :
22
Ted:
20
18
Distance (m)
16
5. Complete the following sentence:
14
Because Bob was traveling at a constant
____________, the shape of his graph line
on the distance—time (speed) graph is a
_________________ line. Ted’s motion
however, was not one of constant speed,
but of _________________. Because Ted
was continuously increasing his speed, his
graph line is the shape of a ___________.
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
Time (s)
Graph 2
Velocity as a Function of Time (Acceleration Graph)
Legend
Speed (m/s)
8
7
Bob :
6
Ted:
5
4
3
2
1
0
0
1
2
3
4
5
6
Time (s)
3
7
8
9
6. On this velocity-time (acceleration)
graph, how does the graph line Bob made
compare to the graph line that Ted made?
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