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Class PH1110A2007
Assignment 5
Due at 5:00pm on Friday, September 7, 2007
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A Wild Ride
A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the
x
axis be parallel to
the ground and the positive
y
axis point upward. In the time interval from
to
s, the trajectory of the car along a
certain section of the track is given by
,
where
is a positive dimensionless constant.
Part A
At
is the roller coaster car ascending or descending?
Hint A.1 How to approach the problem
The direction of motion of a particle is given by the direction of its velocity. In this particular case, you need to
establish if velocity of the car points upward or downward. That can be easily determined by simply looking at the
sign of the vertical component of the velocity of the car.
Part A.2 Find the vertical component of the velocity of the car
Find the
y
component of the velocity of the car,
, at
.
Hint A.2.a Velocity components
Hint not displayed
Express your answer in meters per second in terms of
.
ANSWER:
=
Answer not displayed
ANSWER:
ascending
descending
Part B
Derive a general expression for the speed
of the car.
Hint B.1 How to approach the problem
The speed of a particle is the magnitude of the velocity vector of the particle. Since the magnitude of a vector depends
on its components, to find the speed of the car you need to know the components of the car's velocity.
Hint B.2 Magnitude of a vector
The magnitude of a vector
, whose components are
and
, is given by
.

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Part B.3 Find the components of the velocity of the car
Find a general expression for
and
, that is, the

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