### Understanding Velocity and Acceleration from a Quadratic EquationThe velocity of a particle is given by the equation:\[ v = 39t^2 - 93t + 47 \]where:- \( v \) is the velocity in meters per second (m/s)- \( t \) is the time in seconds (s)#### Task:Plot the velocity \( v \) and acceleration \( a \) versus time for the first 3 seconds of motion. Evaluate the velocity when acceleration \( a \) is zero. After plotting the data, answer the following questions:### Questions:1. **When \( t = 0.5 \) seconds:** - **Velocity \( v \):** \[ v = 10.25 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -73.5 \, \text{m/s}^2 \]2. **When \( t = 1.3 \) seconds:** - **Velocity \( v \):** \[ v = -7.99 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -42.3 \, \text{m/s}^2 \]3. **When \( t = 2.3 \) seconds:** - **Velocity \( v \):** \[ v = 39.41 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -3.3 \, \text{m/s}^2 \]4. **When \( a = 0 \):** - **Velocity \( v \):** \[ v = 895.6 \, \text{m/s} \]#### Graphs and Diagrams:1. **Velocity vs. Time Plot:** - Plot a graph of velocity \( v \) on the vertical axis vs. time \( t \) on the horizontal axis for \( t \) ranging from 0 to 3 seconds. - Mark the points: - \( (0.5, 10.25) \) - \( (1.3, -7.99) \) - \( (2.3, 39.41) \)2. **Acceleration vs

Drawing the velocity and acceleration versus time for the first 3 seconds of motion and calculating…

The velocity of a particle is given by v= 39t2-93t+47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V= 10.25 m/s, a = i -73.5 m/s² When t = 1.3 s, V= -7.99 m/s, a = i -42.3 m/s² When t = 2.3 s, V = 39.41 m/s, a= i -3.3 m/s² When a = 0, V= i m/s 895.6

The velocity of a particle is given by v= 39t2-93t+47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V= 10.25 m/s, a = i -73.5 m/s² When t = 1.3 s, V= -7.99 m/s, a = i -42.3 m/s² When t = 2.3 s, V = 39.41 m/s, a= i -3.3 m/s² When a = 0, V= i m/s 895.6

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: 1. The velocity of a car is given by v(f) = 60(1– (0.7)*), where v is measured in m/s and t is…

Q: The acceleration of a particle is given by a = 2t -21, where a is in meters per second squared and…

Q: The velocity of a particle which moves along the s-axis is given by v = 2 – 5t + 5t7, where t is in…

Q: The displacement of a particle is given by s=4t³-46t2 +95t-37 where s is in feet and t is in…

A: Introduction: Displacement is a vector that points from an object's beginning location to its end…

Q: The displacement of a particle is given by s = 4t³-48t² + 80t -63 where s is in feet and t is in…

A: Write the expression of displacement. s=4t3-48t2+80t-63

Q: Choose correct answer: The motion of a particle is given by :V = 4t2+ 6, where (V) is the velocity…

A: Choose correct answer: The motion of a particle is given by :V = 4t2+ 6, where (V) is the velocity…

Q: The displacement of a particle is given by s = 4t³ - 60t² + 100t - 58 where s is in feet and t is in…

Q: A particle moves along a straight line with a velocity in millimeters per second given by v = 465 -…

Q: )A race car starts accelerating at a = 5 and continues to do this for 10 seconds. What is its final…

Q: If a = (s) m/s?, where s is in meters, determine velocity v in mls when s = 15.5 m. For s = 4.6 m, v…

A: Calculated velocity v in m/s .

Q: A particle moves along a straight line with a velocity in millimeters per second given by v = 413 -…

Q: The displacement of a particle is given by s = 5t - 54t2 + 108t - 44 where s is in feet and t is in…

Q: The displacement of a particle is given by s = 3t - 50t² + 91t - 53 where s is in feet and t is in…

Q: cannon is fired so that a cannonball is launched with a horizontal velocity of +27.5 m/s and a…

A: For the solution refer below images.

Q: The displacement of a particle is given by s = 3t³ - 48t² + 95t-43 where s is in feet and t is in…

A: According to the given dataWe need to findAt t= 2 seconds s,v and aAt t= 6.2 seconds s,v and aAt…

Q: The v-t graph for the motion of a car as it moves along a straight road is shown. Draw the s-t graph…

Q: The position of a particle is given by s = 0.37t- 0.58t² - 2.45t + 5.26, where s is in feet and the…

Q: 4. The motion of a particle starting from the origin is defined by 3x = (y – 2)² , determine its…

A: Motion of the particle is given by 3x=y-22 Differentiate the above equation with respect to x to…

Q: A particle travels along a straight line with a velocity v = (12 – 3t² ) m/s, where t is in seconds.…

Q: If a ball is thrown into the air with a velocity of 52 ft/s, its height in feet t seconds later is…

A: Given data: Velocity = 52 ft·s-1 Height in feet t seconds later is given as = yt =52t-16t2

Q: The a-t graph shown in the figure describes the motion of the airplane as it lands on the runway.…

A: Since in the question the acceleration for a part is not constant, thus we cannot use the three…

Q: (B - Odd) The velocity of a particle which moves along the x axis is given by v = 2 – 4t + 5 t2,…

A: Given, Velocity of particle as a function of time = v(t) = 2 - 4 t + 5 t32 ft/s Initial position =…

Q: The trajectory of a rocket as a function of time given by: 7(t) (1.3 ² + 0.4 ³ ) i +0.4 j = The…

Q: the displacement histories for the 2.0 seconds. Find the time t when the particle crosses the…

Q: (b)Given the shown v-t diagram (1) construct a-t and s-t diagram (II) Using diagrams, find total…

Q: The position of a particle is given by s = 0.39t3 - 0.61t2 - 2.32t + 5.24, where s is in feet and…

A: Calculated velocity and acceleration at t= 0.9 second and velocity and acceleration at t= 3.1…

Q: 4. A girl tosses a ball at an initial velocity of A = 8 ft/s at an angle of 0 = 25°. A boy catches…

A: For solution refer below images.

Q: In reference to the figure, A 0.125 m 0.175 m B Vo = 10 m/s 30° Determine the velocity in m/s of…

Q: A particle starts from rest at x = -2.0 m and moves along the x-axis with the velocity history…

Q: train that starts

A: part -A x=0 m part-B x=-2 m

Q: The motion of a particle is given by :V = 3t2+6, where (V) is the velocity in m/s and (t) is the…

A: V=3t2+6t=1sec

Q: The position of a particle that moves in free fall motion is defined by x = -3t² + 12t - 6 m, where…

A: Relation between position and time is given. For the time interval t = 0s to 3s, it is required to…

Q: 1- A particle moves along the x axis. Its position varies with time according to the expression x= -…

A: Given data The position of the particle is given byx = -4t + 2t2A) We have to find the displacement…

Q: If the velocities are plotted from some an arbitrary point , a curve formed of end points of these…

A: Given Statement :- If the velocities are plotted from some an arbitrary point, a curve formed of…

Q: The position of a particle is given by s = 0.23t³ -0.77t² -2.50t + 5.65, where s is in feet and the…

Q: The velocity of a particle is given by v = 15t2-94t + 63, where v is in meters per second and tis in…

Q: A particle moves along a straight line with a velocity of +(6+2) ft/s, where t is in seconds. What i…

A: velocity (v) = +(6t2) ft/s1-D straight line motion is performed.

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

### Understanding Velocity and Acceleration from a Quadratic Equation

The velocity of a particle is given by the equation:

\[ v = 39t^2 - 93t + 47 \]

where:
- \( v \) is the velocity in meters per second (m/s)
- \( t \) is the time in seconds (s)

#### Task:
Plot the velocity \( v \) and acceleration \( a \) versus time for the first 3 seconds of motion. Evaluate the velocity when acceleration \( a \) is zero. After plotting the data, answer the following questions:

### Questions:

1. **When \( t = 0.5 \) seconds:**
- **Velocity \( v \):**
\[ v = 10.25 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -73.5 \, \text{m/s}^2 \]

2. **When \( t = 1.3 \) seconds:**
- **Velocity \( v \):**
\[ v = -7.99 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -42.3 \, \text{m/s}^2 \]

3. **When \( t = 2.3 \) seconds:**
- **Velocity \( v \):**
\[ v = 39.41 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -3.3 \, \text{m/s}^2 \]

4. **When \( a = 0 \):**
- **Velocity \( v \):**
\[ v = 895.6 \, \text{m/s} \]

#### Graphs and Diagrams:

1. **Velocity vs. Time Plot:**
- Plot a graph of velocity \( v \) on the vertical axis vs. time \( t \) on the horizontal axis for \( t \) ranging from 0 to 3 seconds.
- Mark the points:
- \( (0.5, 10.25) \)
- \( (1.3, -7.99) \)
- \( (2.3, 39.41) \)

2. **Acceleration vs

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

pls help me answer this question this is too hard for me
The velocity of a particle is given by v = 39t2-93t+ 47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V = 10.25 m/s, a= -54 m/s² When t = 1.3 s, V= -7.99 m/s, a = 8.4 m/s² When t = 2.3 s, V= 39.41 m/s, a = 86.64 m/s² When a = 0, V= i 58.25 m/s
SHOW FULL SOLUTION
The displacement of a particle is given by s = 3t³ - 47t² +88t - 61 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 3.3 sec, S = i At t = 7.2 sec, Att = 11.9 sec, S= i S= i The velocity is zero when t = i ft, v = ft, v = i i ft, v = i sec and when t = i ft/sec, a = ft/sec, a = i ft/sec, a = i sec ft/sec ft/sec ft/sec
After a vigorous soccer match, Tina and Michael decide to have a glass of their favorite refreshment. They each run in a straight line along the indicated paths at a speed of 10 ft/sec. Tina Michael Michael Write parametric equations for the motion of Tina and Michael individually after t seconds. (Round all numerical values to four decimal places as needed.) X = Tina y = Michael X = (-50, 200) ● beet juice y = -0.4286t+ 128.5714 ● (200, 300) soy milk (300, 50) Find when Tina and Michael are closest to one another. (Round your answer to four decimal places.) t = S (x, y) = Tina Find where Tina and Michael are closest to one another. (Round your answers to three decimal places.) (x, y) =
help! please write the complete solutions. Thumbs-up willl be given! DYNAMICS OF RIGID BODIES! The equation below gives the velocity of a particle that moves along a straight line. Find the particle's position at x = π seconds.Write answer to the nearest whole number and in m/s2.
i need the answer quickly
The model of a river is constructed to a scale of 1/60. If the water in the river flows at 38 ft/s, how fast must the water flow in the model (ft/s)?
The velocity distance graph for the car moving on a linear path is shown in Figure 3. Determine the rate of change of velocity of car at distance (P)=100 m and distance (P)=200 m. Also draw the acceleration distance diagram.
11(a) The displacement of a particle is given by s = 2t3 - 43t2 + 118t - 64 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 19 seconds of motion. After you have made the plots, answer the questions.
A particle's displacement is defined as s = 2t3 - 30t2 + 100t -50, where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration of the first 12 seconds of motion as functions of time. Calculate the time when the velocity is equal to zero. (t1 at v=0) and (t2 at v=0)
I need help with this question please. thank you