# 2.8 Graphical analysis of one-dimensional motion  (Page 4/8)

 Page 4 / 8

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.

## Section summary

• Graphs of motion can be used to analyze motion.
• 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 ( ${t}_{a}$ , ${t}_{b}$ , ${t}_{c}$ , ${t}_{d}$ , or ${t}_{e}$ ) 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 ( ${t}_{a}$ , ${t}_{b}$ , ${t}_{c}$ , 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 ( ${t}_{a}$ , ${t}_{b}$ , ${t}_{c}$ , 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.

## Problems&Exercises

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 $5\text{.}{\text{0 m/s}}^{2}$ .

(a) $\text{115 m/s}$

(b) $5\text{.}{\text{0 m/s}}^{2}$

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.

$v=\frac{\left(\text{11.7}-6.95\right)×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m}}{\left(40\text{.}\text{0 – 20}.0\right)\phantom{\rule{0.25em}{0ex}}\text{s}}=\text{238 m/s}$

By taking the slope of the curve in [link] , verify that the acceleration is $3\text{.}2 m{\text{/s}}^{2}$ at $t=\text{10 s}$ .

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 $t=2\text{.}5 s$ . (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 $t=5 s$ ? (c) What is his average acceleration between 0 and 4 s? (d) What is his time for the race?

(a) 6 m/s

(b) 12 m/s

(c) ${\text{3 m/s}}^{2}$

(d) 10 s

[link] shows the displacement graph for a particle for 5 s. Draw the corresponding velocity and acceleration graphs.

hello friends what is hadronic heating systems
Hydronics is the use of a liquid heat-transfer medium in heating and cooling systems.
Balogun
what is mass
is the amount of an object
Sendawula
mass is the measure of the inertia of a body
Ishmeal
advantages of CRO over ordinary voltmeter
what is the difference between displacement and distance?!
what is equilibrium
If a system is said to be under equilibrium whenever there is no force act upon it... And it remain in its initial stage..
soniya
what is velocity
Ahmed
time rate of displacement of a body is called velocity
velocity is the gradient of acceleration time graph
Etana
actually equilibrium is when a body is in total balance where in no external force is acting on it. Or the forces on the left hand side equal those on the left hand side and downward forces equal upward forces & anticlockwise moment equal clockwise moment about the same point.
Etana
I mean left hand side and right hand side
Etana
What is conductivity
It is the ease with which electrical charges or heat can be transmitted through a material or a solution.
Cffrrcvccgg
how to find magnitude and direction
how to caclculate for speed
Arjune
derivation of ohms law
derivation of resistance
Kazeem
R=v/I where R=resistor, v=voltage, I=current
Kazeem
magnitude
Arjune
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
Electric current is the flow of electrons
is there really flow of electrons exist?
babar
Yes It exists
Cffrrcvccgg
explain plz how electrons flow
babar
if electron flows from where first come and end the first one
babar
an electron will flow accross a conductor because or when it posseses kinectic energy
Cffrrcvccgg
electron can not flow jist trasmit electrical energy
ghulam
free electrons of conductor
ankita
electric means the flow heat current.
electric means the flow of heat current in a circuit.
Serah
What is electric
electric means?
ghulam
electric means the flow of heat current in a circuit.
Serah
electric means the flow of electric current through conductor
the continuos flow of electrons in a circuit is called electric
ANUBHA
electric means charge
ghulam
electric means current
flow of current.
Sendawula
a boy cycles continuously through a distance of 1.0km in 5minutes. calculate his average speed in ms-1(meter per second). how do I solve this
speed = distance/time be sure to convert the km to m and minutes to seconds check my utube video "mathwithmrv speed"
PhysicswithMrV
d=1.0km÷1000=0.001 t=5×60=300s s=d\t s=0.001/300=0.0000033m\s
Serah
A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t 0 s, the x components of the puck’s ini￾tial velocity and acceleration are v0x 1.0 m/s and ax 2.0 m/s2 . The y components of the puck’s initial velocity and acceleration are v0y 2.0 m/s and ay 2.0
Arjune
D=1km=1000m t=5mins×60secs=300sec s=d/t=3.333m/s
Daniel
I think Daniel Glorious is ryt
Amalia
why we cannot use DC instead of AC in a transformer
becuse the d .c cannot travel for long distance trnsmission
ghulam
what is physics
branch of science which deals with matter energy and their relationship between them
ghulam
Life science
the
what is heat and temperature