Acceleration Word Problems
Average velocity =
Δx x f − xi
=
Δt t f − ti
Δx = vi t + 12 a t 2
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Average acceleration =
Δv v f − vi
=
Δt t f − ti
g = 10. m/s2
v f 2 = vi 2 + 2a Δx
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1. A high-speed cosmic ray hits earth’s atmosphere at a speed of 1.5x108 m/s. If the cosmic ray
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takes 2x10-4 seconds to come to a stop in our atmosphere, what is the ray’s acceleration?
Quantities, with units Symbolic Equation
Quantities (units!) plugged in Answer (unit!)
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2. We are creeping through a cave, when we find a deep hole in the floor. If we drop a rock, we
don’t hear it hit bottom until some time t later.
A. Write a symbolic formula for the depth d of this hole.
B. Suppose the time t is 2.5 seconds. Plug the known quantities in to the formula from part A, and
show the proper answer. (Remember: g is a known quantity!)
C. Write a formula for vf, the speed of the rock when it got to the bottom. Then plug the known
quantities into the formula and write the correct answer.
D. Sketch a position graph and a velocity graph for this motion. Be quantitative (use numbers).
d
v
t
t
E. If we threw the rock down instead of simply dropping it, the formula you wrote in part A
would not give the right answer. Why not?
3. A model rocket starts at rest, and accelerates at 75 m/s2 as it climbs to an altitude of 120 m. What
is the velocity at the 120 m height? Show your work properly.
4. In 1935, a French destroyer, La Terrible, started from rest and accelerated to attain a final speed vf. This
took a time t.
A. How much was La Terrible’s acceleration? Write a symbolic formula for a.
B. La Terrible attained a speed of 83 km/h. Convert this to m/s (use factor conversion method (FCM)).
C. The acceleration took two minutes. Convert this time to seconds, using the FCM.
D. Show your converted quantities plugged in to the formula you wrote in part A, and the correct
answer (remember, to be correct, it must include units!).
E. Write a formula for d, the distance traveled by La Terrible as it accelerates for those two minutes.
Plug in known quantities and write the correct answer.
F. Sketch a position graph and a velocity graph for this motion. Be quantitative (use numbers).
d
v
t
5. A four-man kayak team traveling at a speed oft vi stops rowing, and their speed slows down to vf. This
takes the team a time t.
A. What is the kayak’s acceleration? Write a symbolic formula for a in terms of vi, vf, and t.
B. Suppose the speeds are vo = +9. m/s. and vf is +4 m/s, and the time t = 30. s. Plug in these quantities,
and write the proper answer.
C. Write a formula for the distance d traveled by the kayak during this time, then plug in the known
quantities and write the proper answer.
D. Sketch a position graph and a velocity graph for the kayak. Be quantitative (use numbers).
v
d
t
t
E. Suppose that instead of gradually slowing, the kayak runs into a dock and stops, in a much shorter
time. Use the formula from part A to explain why the acceleration would be greater.