Kinematics
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Obtain the equation for displacement as a function of time with constant velocity from the expression of
instantaneous velocity.
Obtain the expression for displacement as a function of time with constant acceleration from the expression
of instantaneous acceleration.
The speed of a body is given by
\[
\begin{gather}
v=t^3-4t^2+2t+5
\end{gather}
\]
a) What is the position of the body at t = 3 s, if initially it is at x = 6 m?b) What is the acceleration of the body at t = 3 s?
A body moves with acceleration given by
\[
\begin{gather}
a=\alpha-\beta v
\end{gather}
\]
α and β are real positive constants that make the expression dimensionally consistent. Determine
the expressions for the velocity and displacement as a function of time.
Two bodies are in a straight line with constant acceleration on the same trajectory, their motions are
described by the equations
\[
\begin{gather}
\left.
\begin{array}{l}
x_1=2t-\dfrac{1}{2}t^2\\
x_2=10-3t+\dfrac{3}{2}t^2
\end{array}
\right.
\qquad\text{(S.I. units)}
\end{gather}
\]
Determine:
a) The position where they meet;
b) The instant of time that the distance between the two bodies is the smallest and the distance between them;
c) The instant of time in which the speeds of the bodies change direction and their positions.
a) The position where they meet;
b) The instant of time that the distance between the two bodies is the smallest and the distance between them;
c) The instant of time in which the speeds of the bodies change direction and their positions.
A body moves with acceleration given by
\[
\begin{gather}
a=\alpha x
\end{gather}
\]
where α is a positive real constant that makes the expression dimensionally consistent. The
initial velocity of the body is equal to v0 at position x0. Determine
the expression for velocity as a function of position.
A steamboat, sails at a constant speed v (km/h), and consumes 0.3 + 0.001v3 tonnes
of coal per hour. Calculate:
a) The speed that should have a 1000 km route to have a minimum consumption;
b) The amount of coal consumed on this trip.
a) The speed that should have a 1000 km route to have a minimum consumption;
b) The amount of coal consumed on this trip.
Two particles run perpendicular to each other trajectories that intersect at a common origin. The particles
leave at the same time from points x0 and y0 toward the origin, both
with the same constant acceleration in magnitude. Calculate:
a) After how long after they leave they will be at the smallest distance;
b) What is the smallest distance.
a) After how long after they leave they will be at the smallest distance;
b) What is the smallest distance.
A particle is on a plane xy, initially at rest in the position x0 on the positive
x-axis. It begins to move with constant velocities vx, in the direction of origin,
and vy in the direction of the positive y-axis. Determine after how long the
particle will be at the minimum distance of the origin and, what is this minimum distance.
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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 .