A graph of velocity vs. time of a ship coming into a harbor is shown below. (a) Describe the motion of the ship based on the graph. (b)What would a graph of the ship’s acceleration look like?
(a) The ship moves at constant velocity and then begins to decelerate at a constant rate. At some point, its deceleration rate decreases. It maintains this lower deceleration rate until it stops moving.
(b) A graph of acceleration vs. time would show zero acceleration in the first leg, large and constant negative acceleration in the second leg, and constant negative acceleration.
Graphical solutions yield identical solutions to mathematical methods for deriving motion equations.
The slope of a graph of displacement
$x$ vs. time
$t$ is velocity
$v$.
The slope of a graph of velocity
$v$
vs. time
$t$ graph is acceleration
$a$.
Average velocity, instantaneous velocity, and acceleration can all be obtained by analyzing graphs.
Conceptual questions
(a) Explain how you can use the graph of position versus time in
[link] to describe the change in velocity over time. Identify (b) the time (
${t}_{\mathrm{a}}$ ,
${t}_{\mathrm{b}}$ ,
${t}_{\mathrm{c}}$ ,
${t}_{\mathrm{d}}$ , or
${t}_{\mathrm{e}}$ ) at which the instantaneous velocity is greatest, (c) the time at which it is zero, and (d) the time at which it is negative.
(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in
[link] . (b) Identify the time or times (
${t}_{\mathrm{a}}$ ,
${t}_{\mathrm{b}}$ ,
${t}_{\mathrm{c}}$ , etc.) at which the instantaneous velocity is greatest. (c) At which times is it zero? (d) At which times is it negative?
(a) Explain how you can determine the acceleration over time from a velocity versus time graph such as the one in
[link] . (b) Based on the graph, how does acceleration change over time?
(a) Sketch a graph of acceleration versus time corresponding to the graph of velocity versus time given in
[link] . (b) Identify the time or times (
${t}_{\mathrm{a}}$ ,
${t}_{\mathrm{b}}$ ,
${t}_{\mathrm{c}}$ , etc.) at which the acceleration is greatest. (c) At which times is it zero? (d) At which times is it negative?
Consider the velocity vs. time graph of a person in an elevator shown in
[link] . Suppose the elevator is initially at rest. It then accelerates for 3 seconds, maintains that velocity for 15 seconds, then decelerates for 5 seconds until it stops. The acceleration for the entire trip is not constant so we cannot use the equations of motion from
Motion Equations for Constant Acceleration in One Dimension for the complete trip. (We could, however, use them in the three individual sections where acceleration is a constant.) Sketch graphs of (a) position vs. time and (b) acceleration vs. time for this trip.
A cylinder is given a push and then rolls up an inclined plane. If the origin is the starting point, sketch the position, velocity, and acceleration of the cylinder vs. time as it goes up and then down the plane.
Note: There is always uncertainty in numbers taken from graphs. If your answers differ from expected values, examine them to see if they are within data extraction uncertainties estimated by you.
(a) By taking the slope of the curve in
[link] , verify that the velocity of the jet car is 115 m/s at
$t=\text{20 s}$ . (b) By taking the slope of the curve at any point in
[link] , verify that the jet car’s acceleration is
$5\text{.}{\text{0 m/s}}^{2}$ .
Using approximate values, calculate the slope of the curve in
[link] to verify that the velocity at
$t=\text{10.0 s}$ is 0.208 m/s. Assume all values are known to 3 significant figures.
Using approximate values, calculate the slope of the curve in
[link] to verify that the velocity at
$t=\text{30.0 s}$ is 0.238 m/s. Assume all values are known to 3 significant figures.
Construct the displacement graph for the subway shuttle train as shown in
[link] (a). Your graph should show the position of the train, in kilometers, from t = 0 to 20 s. You will need to use the information on acceleration and velocity given in the examples for this figure.
(a) Take the slope of the curve in
[link] to find the jogger’s velocity at
$t=2\text{.}\mathrm{5\; s}$ . (b) Repeat at 7.5 s. These values must be consistent with the graph in
[link] .
A graph of
$v\left(t\right)$ is shown for a world-class track sprinter in a 100-m race. (See
[link] ). (a) What is his average velocity for the first 4 s? (b) What is his instantaneous velocity at
$t=\mathrm{5\; s}$ ? (c) What is his average acceleration between 0 and 4 s? (d) What is his time for the race?
Is there a formula for time of free fall given that the body has initial velocity? In other words, formula for time that takes a downward-shot projectile to hit the ground. Thanks!
2 forces whose resultant is 100N, are at right angle to each other .if one of them makes an angle of 30 degree with the resultant determine it's magnitude
The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool that was in use in Europe, China and Russia, centuries before the adoption of the written Hindu–Arabic numeral system
a load of 20N on a wire of cross sectional area 8×10^-7m produces an extension of 10.4m. calculate the young modules of the material of the wire is of length 5m
Young's modulus = stress/strain
strain = extension/length (x/l)
stress = force/area (F/A)
stress/strain is F l/A x
El
so solve it
Ebenezer
please
Ebenezer
two bodies x and y start from rest and move with uniform acceleration of a and 4a respectively. if the bodies cover the same distance in terms of tx and ty what is the ratio of tx to ty
The atoms which form the element Cesium are known as Cesium atoms.
Naman
A material that combines with and removes trace gases from vacuum tubes.
Shankar
what is difference between entropy and heat capacity
Varun
Heat capacity can be defined as the amount of thermal energy required to warm the sample by 1°C. entropy is the disorder of the system. heat capacity is high when the disorder is high.
The quantum realm, also called the quantum scale, is a term of art inphysics referring to scales where quantum mechanical effects become important when studied as an isolated system. Typically, this means distances of 100 nanometers (10−9meters) or less or at very low temperature.
i want know physics practically where used in daily life
Vinodhini
I want to teach physics very interesting to studentd
Vinodhini
how can you build interest in physics
Prince
by reading it
Austin
understanding difficult
Vinodhini
vinodhini mam, physics is used in our day to day life in all events..... everything happening around us can be explained in the base of physics.....
saying simple stories happening in our daily life and relating it to physics and questioning students about how or why its happening like that can make
revolutionary
your class more interesting
revolutionary
anything send about physics daily life
Vinodhini
How to understand easily
Vinodhini
check out "LMES" youtube channel
revolutionary
even when you see this message in your phone...it works accord to a physics principle. you touch screen works based on physics, your internet works based on physics, etc....... check out google and search for it
revolutionary
what is mean by Newtonian principle of Relativity?
definition and explanation with example
mechanical energy is of two types 1: kinetic energy 2: potential energy,so, potential energy is actually the type of mechanical energy ,the mechanical due to position is designated as potential energy
Iram
Thank you!!!!!
Nikki
Can someone possibly walk me through this problem?
" A worker drives a 0.500 kg spike into a rail tie with a 2.50 kg sledgehammer. The hammer hits the spike with a speed of 65.0 m/s. If one-third Of the hammer's kinetic energy is converted to the internal energy of rhe hammer and spike.
Nikki
how much does the total internal energy increase
Nikki
you know the mass and the velocity of the hammer. therefore using the equation (mv^2)/2 you can find the kinetic energy. then take one third of this value and that will be your change in internal energy. here, the important thing is that spike is stationary so it does not contribute to initial Energ