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Putnam
1946 Putnam
A6
A6
Part of
1946 Putnam
Problems
(1)
Putnam 1946 A6
Source: Putnam 1946
3/13/2022
A particle of unit mass moves on a straight line under the action of a force which is a function
f
(
v
)
f(v)
f
(
v
)
of the velocity
v
v
v
of the particle, but the form of the function is not known. A motion is observed, and the distance
x
x
x
covered in time
t
t
t
satisfies the formula
x
=
a
t
2
+
b
t
+
c
x= at^2 + bt+c
x
=
a
t
2
+
b
t
+
c
, where
a
,
b
,
c
a,b,c
a
,
b
,
c
have numerical values determined by observation of the motion. Find the function
f
(
v
)
f(v)
f
(
v
)
for the range of
v
v
v
covered by the experiment.
Putnam
function
physics