A particle initially located at the origin has an acceleration of **\[ \vec{a} = -4.00 \hat{\jmath} \, \text{m/s}^2 \]** and an initial velocity of **\[ \vec{v}_i = 9.00 \hat{\imath} \, \text{m/s} \]**.(a) Find the vector position of the particle at any time \( t \) (where \( t \) is measured in seconds).\[ (\_\_\_\_ \, t \hat{\imath} + \_\_\_\_ \, t^2 \hat{\jmath}) \, \text{m} \](b) Find the velocity of the particle at any time \( t \).\[ (\_\_\_\_ \, \hat{\imath} + \_\_\_\_ \, t \hat{\jmath}) \, \text{m/s} \](c) Find the coordinates of the particle at \( t = 6.00 \, \text{s} \).\[ x = \_\_\_\_ \, \text{m} \]\[ y = \_\_\_\_ \, \text{m} \](d) Find the speed of the particle at \( t = 6.00 \, \text{s} \).\[ \_\_\_\_ \, \text{m/s} \] **Need Help?** - [Read it]- [Watch it]

Name: A particle initially located at the origin has an acceleration of **\
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: A particle initially located at the origin has an acceleration of **\[ \vec{a} = -4.00 \hat{\jmath} \, \text{m/s}^2 \]** and an initial velocity of **\[ \vec{v}_i = 9.00 \hat{\imath} \, \text{m/s} \]**.(a) Find the vector position of the particle at

(a) Position of the particle is : r→f= ri→ +vit→ +12at2 =0+9t i^+ 12(4)t2 j^ = 9t i ^…

Science

Physics

A particle initially located at the origin has an acceleration of a = 4.00j m/s2 and an initial velocity of v = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî+ 2 j) m (b) Find the velocity of the particle at any time t. t j) m/s (c) Find the coordinates of the particle att = 6.00 s. X%3= y = m (d) Find the speed of the particle at t = 6.00 s. m/s

A particle initially located at the origin has an acceleration of a = 4.00j m/s2 and an initial velocity of v = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî+ 2 j) m (b) Find the velocity of the particle at any time t. t j) m/s (c) Find the coordinates of the particle att = 6.00 s. X%3= y = m (d) Find the speed of the particle at t = 6.00 s. m/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: The vector position of a particle varies in time according to the expression 7(t)=(1.76 t + 1.56)7…

A: Given data: The equation of particle which varies in time is given as, The equation of velocity…

Q: Given a displacement Vector F(t)= (2.50 m)1 + (0.25 m/s³)t³ (6.00 m/s)tk Find the displacement, Keep…

A: The displacement is given by, r(t)→=2.5i^+0.25t3j^-6tk^. Where r is in meter and t is in sec.…

Q: The position of a particle in space at time tis: r(t) = (sec(t)) * i + (tan t) * j + 4/3 tk. Write…

A: Given: The position of the particle is rt=secti+tantj+43tk…

Q: A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with…

Q: Let the position vector (with its tail at the origin) of a moving particle be ~r(t) = t^(2)ˆi − 2tˆj…

Q: A particle initially located at the origin has an acceleration of = 1.00ĵ m/s2 and an initial…

A: Here, it is given that, initial location of the particle: origin Initial velocity of the particle: 9…

Q: average velocity during the time interval from t = 1.85 s to t = 3.85 s

A: Given: Position vector as a function of time rt=xti^+ytj^ Where xt=at+b and yt=ct2+d Values of…

Q: Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ,…

Q: Two particles have position vectors given by 7 = 2tê, - t'e, + (3t2 - 4t) ê, , = (5t2 - 12t + 4)ê, +…

Q: A snowmobile is originally at the point with position vector 26.5 m at 95.0\deg counterclockwise…

Q: Suppose the position vector for a particle is given as a function of time by F(c) =…

Q: A particle initially located at the origin has an acceleration of a - 2.00j m/s? and an initial…

Q: 1. A particle initially located at the origin has a constant acceleration of a = 3.00j m/s and an…

A: Given data The magnitude of the constant acceleration is a = 3 j m/s2 The initial velocity of the…

Q: The vector position of a particle varies in time according to the expression: r =( 20ti+(2 + 20t-5t…

A: The position vector of the particle is given as: r→=20t i^+2+20t-5t2j^ It is required to find its…

Q: A Particle is in the xy-plane in uniform circular motion around the origin. The x- and y-…

Q: Find the position vector of a particle that has the given acceleration and the specified initial…

Q: Position vector of a moving particle is given by r(t)= (2t2−5t+2, 2t2+1,(t+1)2) (a) At what time(s)…

Q: Suppose that a particle's position is described by r(t) = ti+ (t + 1) k. Find the velocity vector…

Q: Ammar flies a drone starting from time = 0 second and position (0, 4m) with an acceleration of ? ⃑ =…

Q: A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one…

Q: The acceleration of a particle is a = (5.00 i - 7.00 j) m/s^2. At t = 0, the particle leaves the…

Q: Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ,…

Q: The velocity V of a particle moving in the xy plane is given by 7 = ( 5.50 t - 5.00 7 )î + 9.00 3.…

A: According to question we need to find--- at which time the velocity of the object will be zero?

Q: 0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: A particle is moving with the given data. Find the position of the particle. = 5 sin t – 2 cos t,…

A: Given: The acceleration is given as, at=5sint-2cost Positions are, s0=0s2π=4

Concept explainers

Projectile Motion

Topic Video

Question

A particle initially located at the origin has an acceleration of **\[ \vec{a} = -4.00 \hat{\jmath} \, \text{m/s}^2 \]** and an initial velocity of **\[ \vec{v}_i = 9.00 \hat{\imath} \, \text{m/s} \]**.

(a) Find the vector position of the particle at any time \( t \) (where \( t \) is measured in seconds).

\[
(\_\_\_\_ \, t \hat{\imath} + \_\_\_\_ \, t^2 \hat{\jmath}) \, \text{m}
\]

(b) Find the velocity of the particle at any time \( t \).

\[
(\_\_\_\_ \, \hat{\imath} + \_\_\_\_ \, t \hat{\jmath}) \, \text{m/s}
\]

(c) Find the coordinates of the particle at \( t = 6.00 \, \text{s} \).

\[
x = \_\_\_\_ \, \text{m}
\]

\[
y = \_\_\_\_ \, \text{m}
\]

(d) Find the speed of the particle at \( t = 6.00 \, \text{s} \).

\[
\_\_\_\_ \, \text{m/s}
\]

**Need Help?**
- [Read it]
- [Watch it]

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

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, physics and related others by exploring similar questions and additional content below.

Similar questions

Suppose that the position vector for a particle is given as a function of time by (t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.05 m, c = 0.117 m/s2, and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.85 s. = m/s (b) Determine the velocity at t = 2.05 s. = m/s Determine the speed at t = 2.05 s. m/s
A particle initially located at the origin has an acceleration of 3.00j m/s² and an initial velocity of 5.00i m/s. Find: a) the vector position of the particle at any time b) the velocity of the particle at any time c) the coordinates of the particle at f= 2.00 s d) the speed of the particle at t = 2.00 s
A body moves from:position (1.0 m)i− (3.0 m)j where its velocity is (2.0 m/s)i+ (0.5 m/s)jto position (−1.0 m)i+ (1.0 m)j where its velocity is (4.0m/s)iExpress the body’s displacement (vector) delta r.Express the body’s change in velocity (vector) delta v.
I need help here please
The coordinates of a particle moving in a plane are given by r = 4 cos 6t and y = 6 sin 6t find the angle between position vector 7 and velocity vector i at time t: = T/12
The vector position of a particle varies in time according to the expression F(t)=(1.41 t + 1.72)i +(0.224t2 + 1.11)J where r is in meters and t is in seconds. Find the speed of the particle in m/s at 2.58 s.
A particle initially located at the origin has an acceleration of a = 1.00j m/s? and an initial velocity of v = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( 6 tî+ +5 t? j) m (b) Find the velocity of the particle at any time t. (6 î + 1 v tj) m/s (c) Find the coordinates of the particle at t = 6.00 s. X = 36 m y = 0 For the y coordinate of the particle, you need to know the y components of the initial position, the velocity, and the acceleration. m (d) Find the speed of the particle at t = 6.00 s. 8.49 m/s
An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.
A particle leaves the origin with an initial velocity 3.00î m/s and a constant acceleration ở -1.00î – 0.50ĵ m/s². When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?
Suppose that a dove is flying so that its acceleration vector at time t is given by a(t)=<t^4, t^3, t^2>, its initial velocity is v(0)=<1,2,3> and its initial displacement is s(0)=<7,6,5>. Find the position vector s(t) at time t.
A particle initially located at the origin has an acceleration of a = 2.00ĵ m/s² and an initial velocity of = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( tî + (²ĵ) m f (b) Find the velocity of the particle at any time t. ( î+ tj) m/s (c) Find the coordinates of the particle at t = 7.00 s. X = y = m m (d) Find the speed of the particle at t = 7.00 s. m/s Submit Answer
Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)j, with x(t) = at + b and y(t) = ct + d, where a = 2.00 m/s, b = 1.15 m, c = 0.116 m/s2, and d = 1.08 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t= 3.80 s. m/s (b) Determine the velocity at t = 2.25 s. v = m/s Determine the speed at t = 2.25 s. m/s