Name:_______________________________ Period:________________ Date:___________
#17 ACCELERATED MOTION WORD PROBLEMS
Your objective for this activity is to practice solving word
problems involving accelerated motion.
PRIOR KNOWLEDGE NEEDED
1.
2.
3.
4.
You need to be familiar with the general method for approaching word problems.
You need to recognize displacement, distance, velocity, speed and acceleration from their units.
You need to recognize variables from their abbreviations.
You should be able to recognize the connections between the more general forms of the motion
equations and the simpler ones we used in the previous unit.
EQUATIONS
OF
𝑎⃗ =
MOTION
𝑣𝑓 − ⃗⃗⃗⃗
⃗⃗⃗⃗⃗
𝑣𝑖
∆𝑣⃗
𝑜𝑟 𝑎⃗ =
(𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛, 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣𝑠. 𝑡𝑖𝑚𝑒 𝑔𝑟𝑎𝑝ℎ)
∆𝑡
𝑡𝑓 − 𝑡𝑖
𝑣⃗ = ⃗⃗⃗⃗
𝑣𝑖 + 𝑎⃗𝑡 (𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦)
𝑣𝑎𝑣 =
⃗⃗⃗⃗⃗⃗⃗
⃗⃗
𝐷
∆𝑃⃗⃗
𝑜𝑟 ⃗⃗⃗⃗⃗⃗⃗
𝑣𝑎𝑣 =
(𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑣𝑠. 𝑡𝑖𝑚𝑒 𝑔𝑟𝑎𝑝ℎ)
∆𝑡
∆𝑡
1
𝑃⃗⃗ = ⃗⃗⃗
𝑃𝑖 + ⃗⃗⃗⃗𝑡
𝑣𝑖 + 2𝑎⃗𝑡 2
In all our problems in this unit, you can assume that the acceleration is constant. You can use a
value of 9.8 m/s/s downward for when the acceleration is due to gravity alone.
SAMPLE PROBLEM
A jumbo jet taxing down a runway receives word that it must return to the gate. The jet is
traveling at 45.0 m/s when the pilot receives the message. What is the acceleration of the plane if
it takes the pilot 5.00 s to bring the plane to a stop?
𝑣𝑖 = 45.0
⃗⃗⃗⃗
𝑣𝑓 = 0.0
⃗⃗⃗⃗⃗
𝑚
𝑠
𝑚
𝑠
𝑓𝑜𝑟𝑤𝑎𝑟𝑑
∆𝑡 = 5.00𝑠
𝑎⃗ =?
1
𝑓𝑜𝑟𝑤𝑎𝑟𝑑
𝑎⃗ =
⃗⃗⃗⃗⃗−𝑣
𝑣𝑓 ⃗⃗⃗⃗𝑖
𝑡𝑓 −𝑡𝑖
𝑎⃗ =
𝑚
𝑠
𝑚
𝑠
0.00 𝑓𝑜𝑟𝑤𝑎𝑟𝑑−45.0 𝑓𝑜𝑟𝑤𝑎𝑟𝑑
5.00 𝑠
= −9.00
𝑚
𝑠2
𝑓𝑜𝑟𝑤𝑎𝑟𝑑 = 9.00
𝑚
𝑠2
𝑏𝑎𝑐𝑘𝑤𝑎𝑟𝑑
Check: acceleration is in opposite direction to motion since plane is slowing
PRACTICE PROBLEMS
For all of these problems you need to show all of your work:





Draw a sketch to identify your choice of positive and negative directions for the motion.
Identify all the variables that you are given and what you are being asked to find with their
units.
Write the equation you will use
Show your algebraic manipulations
Box the correct answer with units and direction if it is a vector.
1. While driving his sports car at 20.0 m/s West down a straight section of four lane highway,
Eddie comes up behind a slow moving dump truck and decides to pass it. If Eddie can speed
up at 5.00 m/s/s, how long will it take him to reach a speed of 30.0 m/s going West?
2. Vivian is walking East to the dentist at 1.3 m/s to the North when she glances at her watch
and realizes she is going to be late. She gradually quickens her pace at a rate of 0.090
m/s/s. What is Vivian’s velocity after 10.0 s? What is the direction of her acceleration?
3. Grace is driving her sports car at 30. m/s South when a ball rolls our into the street in front
of her. She slams on the brakes and comes to a stop in 3.0 s. What was Grace’s
acceleration?
4. If Grace’s acceleration was constant, how far did she travel before stopping?
5. The Steamboat Geyser in Yellowstone is capable of shooting hot water from the ground at a
velocity of 48.0 m/s upward. How high does the stream of water rise before starting back
down? g=9.8 m/s/s downwards.
6. A baby bird is waiting for dinner. Its mother tries to drop a worm in its mouth but the baby
bird misses. It takes the worm 1.50 s to hit the ground. How high up was the nest? g=9.8
m/s/s downwards.
7. Challenge Problem: King Kong carries Fay Wray up the 321 m tall Empire State Building.
At the top of the skyscraper, Fay’s shoe falls from her foot. How fast will the shoe be
moving when it hits the ground? g=9.8 m/s/s downwards.
2