One-dimensional Motion
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Average Speed
The motion of a car, which moves with constant speed, is described by the following table:
| t (h) | 1 | 2 | 4 | 7 | 9 | 11 | 12 |
|---|---|---|---|---|---|---|---|
| S (km) | 100 | 200 | 450 | 600 | 400 | 200 | 100 |
from the table data find:
a) The average speed of the car between the instants 1 h and 2 h;
b) The average speed of the car between the instants 4 h and 7 h;
c) The average speed of the car between the instants 9 h and 12 h;
d) The average speed of the car between the instants 1 and 12 h.
The biggest known star (until June 2019) is VY Canis Majoris in the constellation of Canis Major, with an
estimated diameter of 1,975,000,000 km. Making the (absurd) assumption that a commercial jet could fly close
to the surface of the star at a constant speed of 990 km / h. How long would the jet take for a spin on the
star. Answer in years.
A worker leaves his house and walks for 600 meters in 5 minutes to the bus stop, as soon as he reaches the
bus stop he takes the bus and travels for 40 minutes at a constant speed of 18 kilometers per hour to the
factory where he works. If he took the entire route by bike, at a constant speed of 6 meters per second.
How long would it take from home to the factory? Answer in minutes.
One-Dimensional Motion with Constant Speed
The motion of a body is described by the displacement as a function of time
a) The initial position;
b) The speed;
c) The instant in which the body passes through the origin;
d) The position of the body at time 4 h.
\[
\begin{gather}
S=-10+4 t
\end{gather}
\]
where the position is measured in kilometers and the time in hours. Find:a) The initial position;
b) The speed;
c) The instant in which the body passes through the origin;
d) The position of the body at time 4 h.
A motorcyclist moves in the opposite direction of an oriented frame of reference, the magnitude of its
speed is 40 m/s, and initially, his position is −150 m. Find:
a) The displacement as a function of time;
b) In what time he passes the origin.
a) The displacement as a function of time;
b) In what time he passes the origin.
During a thunderstorm, a man sees lightning but hears thunder 5 seconds later. The speed of sound in air is
constant and equal to 340 m/s. Determine:
a) The distance between the man and the place of lightning;
b) The time it took for light to go from the location of the lightning to the point where the man is. The speed of light equal to 300,000 km/s.
a) The distance between the man and the place of lightning;
b) The time it took for light to go from the location of the lightning to the point where the man is. The speed of light equal to 300,000 km/s.
A high-speed train with a constant speed of 234 km/h runs through a 620 m long tunnel, the length of the
train is 160 m. What is the time interval to cross the tunnel?
Two boats depart from the same point and travel on the same straight line, with a constant speed of 25 km/h
and 35 km/h. Communication between the two boats is possible by radio as long as the distance between them
does not exceed 600 km. Find the time interval during which the two boats can communicate, in the following
cases:
a) The two boats move in the same direction;
b) The slower boat departs two hours before the other and moves in the same direction;
c) The two boats depart at the same time and move in opposite directions.
a) The two boats move in the same direction;
b) The slower boat departs two hours before the other and moves in the same direction;
c) The two boats depart at the same time and move in opposite directions.
During a fog, a navigator receives two signals simultaneously sent by a station on the coast, one through
the air and the other through the water. Between the receptions of the two sounds, an interval of time,
t=5 seconds, elapses. Under the conditions of the experiment, the speed of sound in the air is
341 m/s and 1504 m/s in the water. Determine the distance x between the boat and the station
emitting the signals.
An earthquake generates two types of waves that propagate along the surface. Primary waves (P-wave) travel
at a speed of 8 km/s, and secondary waves (S-wave) travel at a speed of 5 km/s. An observer is at a certain
distance from the earthquake's epicenter and receives the primary waves first, followed by the secondary
waves. How far is the observer from the epicenter if the secondary waves arrive 80 seconds after the primary
waves?
Average Accelaration
The table below describes the velocities of a particle moving in a given reference frame.
| t (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| v (m/s) | 9 | 6 | 3 | 0 | -3 | -6 | -9 |
from the table find:
a) The initial speed of the particle;
b) The instant when the particle changes its direction;
c) The average acceleration of the particle between the instants 1 s and 2 s;
d) The average acceleration of the particle between the instants 5 s and 6 s.
One-Dimensional Motion with Constant Acceleration
A motorcyclist is moving in the opposite direction of a reference frame. The magnitude of its initial speed
is 25 m/s, at the initial time its position is −150 m, and the magnitude of deceleration is
2 m/s2. Determine:
a) The equation of displacement as a function of time;
b) The equation of velocity as a function of time;
c) The instant in which it passes through the origin of the reference frame;
d) The instant that its speed is zero.
a) The equation of displacement as a function of time;
b) The equation of velocity as a function of time;
c) The instant in which it passes through the origin of the reference frame;
d) The instant that its speed is zero.
A car moves along a straight road with a speed of 200 km/h. When this car passes through another car,
initially at rest at a gas station, it begins to move with a constant acceleration of 4.5 m/s2
until it reaches the speed of 200 km/h. Determine:
a) What is the time elapsed until the car leaving the gas station reaches the speed of 200 km/h?
b) How far are they from each other when their speeds are equal?
a) What is the time elapsed until the car leaving the gas station reaches the speed of 200 km/h?
b) How far are they from each other when their speeds are equal?
Two particles move along the same line, with motion given by the following equations
a) The instant of time when the two particles meet;
b) The velocities and accelerations of both at that instant;
c) The position of the meeting point;
d) When and where the velocities of the two particles are equal;
e) The instant of time when the particles change direction.
\[
\begin{gather}
S_1=-10t+5t^2\\[10pt]
S_2=30+5t-10t^2
\end{gather}
\]
the positions are given in centimeters from the origin, and time t is given in seconds.
Determine:a) The instant of time when the two particles meet;
b) The velocities and accelerations of both at that instant;
c) The position of the meeting point;
d) When and where the velocities of the two particles are equal;
e) The instant of time when the particles change direction.
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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 .