One-dimensional Motion
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One-Dimensional Motion with Constant Acceleration
The position of a particle moving at a constant velocity is given at three different times:
\[
\begin{gather}
S = 6\;\mathrm m\quad\text{in}\quad t = 2\;\mathrm s\\
S = 9\;\mathrm m\quad\text{in}\quad t = 4\;\mathrm s\\
S = 33\;\mathrm m\quad\text{in}\quad t = 8\;\mathrm s\\
\end{gather}
\]
What will be the position of the particle at t = 10 s?
A passenger is 5 meters away and runs to try to catch a train that is starting from rest with an acceleration
of 2 m/s2. What must be the passenger's minimum constant speed, vp, to reach the
train?
An object is launched vertically from the top of a building, passing in front of a window 1.50 m high in
0.09 s. The top of the window is at a distance of 13.00 m from the top of the building. What is the initial
velocity of the object?
A particle travels along a path in an accelerated motion. At the instant t = 2 s its velocity is
equal to −4 m/s, at the instant t = 3 s its position is 4.5 m, and at the instants
t = 5 s and t = 7 s its velocities are equal, and of opposite signs. Determine the function
S=f(t) of the motion.
A train leaves station A, where it is at rest, with a constant acceleration equal to a, at one
point, the train driver starts to brake the train with a deceleration equal to b, the train stops at
station B. The distance between the stations is equal to L. Determine the total time it takes
to travel from one station to another.
A car travels with constant acceleration, initial speed v0, and acceleration α.
a) Calculate the distance traveled by car at n-th second (that is, between the instants n-1 and n);
b) For v0 = 15 m/s and α = 1.2 m/s2, calculate the distance traveled in the first second and in the fifteenth second.
a) Calculate the distance traveled by car at n-th second (that is, between the instants n-1 and n);
b) For v0 = 15 m/s and α = 1.2 m/s2, calculate the distance traveled in the first second and in the fifteenth second.
A cyclist A starts a race from the rest, accelerating 0.50 m/s2. At this moment, another
cyclist B passes him, with a constant speed of 5.0 m/s and in the same direction as cyclist A.
a) After how long, after the start, the cyclist A reaches the cyclist B?
b) What is the speed of cyclist A when reaching cyclist B?
a) After how long, after the start, the cyclist A reaches the cyclist B?
b) What is the speed of cyclist A when reaching cyclist B?
Two cars compete in a drag race over a distance of 402 meters (the most common distance for a quarter-mile).
The cars start from rest, with car A having an acceleration of 5 m/s2 and reaching a
maximum speed of 36 m/s, while car B has an acceleration of 4 m/s2 and reaches a maximum
speed of 40 m/s. Determine:a) Which car wins the race?
b) If after the finish line the cars, instead of stopping, continued running, would one of the cars surpass the other?
A car starts a motion from the rest in a straight line. The car runs 100 m and 120 m in two successive
seconds. Determine the acceleration of motion.
From two distant points, A and B, depart one car from each point, its motions are described by
the following equations, measures in International System of Units (S.I.).
b) The speed of each car, when they are at a distance calculated in the previous item.
\[
\begin{gather}
S_{\small A}=10t+\frac{3}{2}t^2\\[10pt]
S_{\small B}=300-2t^2
\end{gather}
\]
a) Determine the distance between cars, when the magnitude of their speeds are equal;b) The speed of each car, when they are at a distance calculated in the previous item.
Two cars depart from distant points A and B, their motions are described by the following
equations
Determine the distance between cars, when the magnitudes of their velocities are the same.
\[
\begin{gather}
S_{\small A}=2t^2\\[10pt]
S_{\small B}=300-2t^2
\end{gather}
\]
units of the International System of Units (S.I.).Determine the distance between cars, when the magnitudes of their velocities are the same.
Two trucks depart from distant points A and B, their motions are described by the following
equations
Determine the distance between trucks when the magnitudes of their velocities are the same.
\[
\begin{gather}
S_{\small A}=10t+3t^2\\[10pt]
S_{\small B}=300-2t^2
\end{gather}
\]
units of the International System of Units (S.I.).Determine the distance between trucks when the magnitudes of their velocities are the same.
Two buses depart from distant points, A and B, their motions are described by the following
equations
a) Determine the distance between the buses when the magnitude of their velocities are equal;
b) The speed of each bus when they are at a distance calculated in the previous item.
\[
\begin{gather}
S_{\small A}=3t^2\\[10pt]
S_{\small B}=300-2t^2
\end{gather}
\]
units of the International System of Units (S.I.).a) Determine the distance between the buses when the magnitude of their velocities are equal;
b) The speed of each bus when they are at a distance calculated in the previous item.
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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .