A particle moves so that its position (in meters) as a function of time (in seconds) is 7 = (6)i + (2r² )j + (8.80t) k. Write %3D expressions (in unit vector notation) for (a) its velocity and (b) its acceleration as functions of time. (a) i i t-j + i (b) i •i + i i <心

A particle moves so that its position (in meters) as a function of time (in seconds) is 7 = (6)i + (2r² )j + (8.80t) k. Write %3D expressions (in unit vector notation) for (a) its velocity and (b) its acceleration as functions of time. (a) i i t-j + i (b) i •i + i i <心

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 11P: A particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in...

See similar textbooks

Related questions

Q: A squirrel has x- and y-coordinates (1.1 m, 3.4 m) at time t, = 0 and coordinates (5.3 m, -0.5 m) at…

A: Given: The initial coordinate of the squirrel is (1.1 m, 3.4 m). The time is t1=0. The final…

Q: 1.1 A particle P moves along the X-axis with acceleration a at a time t given bya =6 ms – 2tms…

Q: In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and…

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

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 * 23t ,…

A: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 * 23t ,…

Q: During the time interval 0 < t < 1, the velocity of an object as a function of time is v = 5 + 3t^2…

A: Given value--- v = 5 + 3t^2 + 2t^3 . We have to find--- Acceleration of an object in terms of t ?

Q: A particle starts from the origin at t = 0 with velocity of 4.5} and moves in the xy plane with a…

Q: A particle moves along the x axis according to the equation x=2.00 + 3.00t - 1.00t², where x is in…

A: Given information: The position of a particle is, x(t)=2.00+3.00t-1.00t2 We have to find the…

Q: Answer the following

A: (a) The velocity of the particle is, v=dxdt ...... (1) The given…

Q: The velocity of an object moving along a line is given by v = 2t2 + 5 ft/s on the interval 0sts4. a.…

Q: The velocity function, in feet per second, is given for a particle moving along a straight line,…

A: (a) The particle’s displacement is simply the shortest distance between its motion’s starting point…

Q: A classic physics problem states that if a projectile is shot vertically up into the air with an…

Q: Over a short interval, starting at time t = 0, the coordinate of an automobile in meters is given by…

A: The veocity is the rate of change of the position with respect to time. ∴ V=dxdt and the…

Q: A particle's position along the x-axis is described by x(t)= At + Bt^2, where t is in seconds, x is…

Q: The coordinate of an object is given as a function of time by x(t) = 6t2 - t3, where x is in meters…

Q: An animal has a coordinates of (1.1 m, 3.4 m) at time t1 = 0 and when t2= 3.0 s, it is located at…

A: Given data: At time t1 =0 x1, y1=(1.1m,3.4m) At time t2 =3.0s x2, y2=(5.3m,-0.5m)

Q: omponent varies as given by the following function: ax(t) = 5t - 2t2 + 45e-t/F, where t is in…

Q: A soccer player kicks a rock horizontally off a cliff 48.0 m high into a pool of water. If the…

A: Given: cliff height, h= 48m time, t = 3.30s initial speed=?So for this…

Q: An annoying spider strolls nonchalantly from an initial position of r; = (-35.5i + 45.0j) cm to a…

A: (given) Initial position of spider rolls = (-35.5 i + 45.0 j) cm Final position of spider rolls =…

Q: An object's position as a function of time is given by the expression; x(t) = 13.9/(t+1) + 2.2t3 -…

A: Average velocity=total displacementtotal time ......(1)

Q: Based on experimental observations, the acceleration of a particle is defined by the relation a…

A: Acceleration is the rate of change of velocity v with respect to time. It is the vector quantity…

Q: A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by y2 =…

A: AIM: To determine the magnitude of acceleration (a) and velocity (v) at a time (t) GIVEN: The…

Q: The motion of a dog is observed to be given by the function = (1.28 m/s²) t²-[(0.66 m/s³) t³-2.99…

Q: An objects position in the x-direction as a function of time is given by the expression: x(t)=5t^2 +…

A: The position of the object, x(t) = 5t2 + 2t The initial time, t1 = 1.15 s The final time, t2 = 2.07…

Q: A particle moves along the positive X-axis. Its speed (V) varies with time as shown in the adjacent…

A: The area under the velocity vs time graph gives the displacement. Calculate the area of trapezoidal.…

Q: ст A particle moves along a straight line and has acceleration given by s"(t) = 4t +3. Its initial…

Q: At t = 0 the coordinates of a particle are x = 0, y = 2.10 m. At a time 1.05 s later, its…

Q: An object moves along the x-axis with an acceleration function of: a(t) = tā + 2 At t seconds. If…

A: Given: The acceleration (a(t)) is given as t1/2 + 2. Introduction: The acceleration (a) of an object…

Q: 2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The velocity function, in feet per second, is given for a particle moving along a straight line,…

A: Given, velocity, v(t)=5t-7, 0≤t≤3.

Q: An object initially found at origin O moves along the x-axis with a velocity of v = (3t^2 6t) m/s,…

A: Given data: Velocity of object V = (3t2 - 6t) m/s

Q: The velocity function v(t) (in meters per second) is given for a particle moving along a line. v(t)…

Q: The position of a particle moving along an x axis is given by x = 12.0t2 - 2.00t3, where x is in…

A: Given data: Position as function of time x = 12.0t2 - 2.00t3 x in meters and t in seconds Required:…

Q: A particle moves along the x-axis according to the equation x = 2.00 +3.00t -1.00t^2, where x is in…

A: Given data: Position of the particle as function of time x = 2.00 + 3.00t - 1.00t2 Time (t) = 3.00…

Q: The motion of a dog is observed to be given by the function = (1.78 m/s) t²i-[(0.46 m/s ) t³-3.5 m…

A: GIVEN: Position function R→ =( 1.78m/s2)t2i^ -(0.46m/s3)t3-3.5m

Q: A particle travels along the x-axis such that its velocity is given by v(t)=t^{1.8}cos(2t). What is…

Q: The position coordinate of a particle which is confined to move along a straight line is given by "x…

Q: A particle’s velocity along the x-axis is described by v(x) = A x + B x2, where x is in meters, v is…

Q: The coordinate of a particle in meters is given by x(t) = 16t – 3.0t³, where the timet is in…

Q: A particle moving along the xx-axis has its position described by the function…

A: Given data: Position of particle in terms of time x = (4t3 + 5t + 2)m Required: The position of…

Q: An object is moving along the x-axis. At t = 0 it is at x = 0. Its x-component of velocity Vx as a…

A: Given Vx(t) = at - Bt3, where a = 6.8 m/s2 and B = 4.0 m/s4 At t=0, X =0

Q: A particle travels along a straight-line path y = 0.7x. If the x component of the particle's…

Q: A particle moves along a horizontal path with a velocity of v = (312- 6t) m/s. where t is the time…

A: The equation for velocity is given by, v=3t2-6t -----1 Here, t is the time in seconds.

Question

Hi I need to understand this problem please with 3 significant digit

A particle moves so that its position (in meters) as a function of time (in seconds) is 7 = (6)i + (2r² )j + (8.80t) k. Write
expressions (in unit vector notation) for (a) its velocity and (b) its acceleration as functions of time.
(a) i
i
t-j + i
(b) i
•i +
i
i

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

A particle moves along an x axis from point A to point B with average velocity v1 = 4.00 m/s through displacement Δx1 = 20.0 m. Then it moves at average velocity v2 through displacement Δx2 = 30.0 m from point B to point C. If the total time is 7.00 s, what is the value of v2?
The position coordinate of a particle which is confined to move along a straight line is given by "x = 2t3 −24t + 6", where x is measured in meters from a convenient origin and t is in seconds. Determine (a) the time required for the particle to reach a velocity of 72 m/s from its initial condition at t = 0 s, (b) the acceleration of the particle when v = 30 m/s, and (c) the net displacement of the particle during the interval from t = 1 s to t = 4 s.
A particle is moving horizontally with constant acceleration. The position (x, in meters) as a function of time (t, in seconds) is given by x= 0.798 t^2 + 0.3552 t + 0.0355. Based on this information, the acceleration of the particle is what?
At t = 0 the coordinates of a particle are x = 0, y = 1.98 m. At a time 0.95 s later, its coordinates are x = 3.21 m, y = 4.20 m. Find the components of the particle's average velocity during this time interval. vx = vy =
A particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.
A blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?
An object has position given by the vector r = [3.0m + (6.0m/s)t] i + [2.0m - (2.0m/s2)t2] j, where quantities are in SI units. What is the speed of the object at t = 3.0s?
On a spacecraft two engines fire for a time of 567 s. One gives the craft an acceleration in the x direction of ax = 4.80 m/s2, while the other produces an acceleration in the y direction of ay = 7.52 m/s2. At the end of the firing period, the craft has velocity components of vx = 3751 m/s and vy = 4834 m/s. Calculate the magnitude of the initial velocity.
Over a short interval, starting at time t = 0.0 s, the coordinate of an automobile in meters is given by x(t) = 27t – 4.0t2, where t is in seconds. The magnitudes of the initial velocity and acceleration of the auto (respectively) are 0.0 m/s, 12 m/s2 0.0 m/s, 24 m/s2 27 m/s, 4.0 m/s2 27 m/s, 8.0 m/s2
In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax(t) = 8t - 2t2 + 15e-t/F, where t is in seconds, ax is in meters per square second, and the constant F is in seconds. At t = 0, the particle was at position x = 3 m with a velocity pointing towards the positive x-axis and having magnitude 25 m/s. In the following problem you can take the constant F = 1.0 s.
At t=0 an object starts from the origin and moves with a constant acceleration of a→=(−3.2i−2.7j)m/s2 on a horizontal surface. If the initial velocity of the object is vo→=(14.1i−18.3j)m/s, determine the magnitude of velocity at t=2.1s. Express your answer in units of m/sm/s using zero decimal places.
A car moves along a horizonatal road with constant velocityv0 = v0, x^ii = (30.06 m/s)^i until it encounters a smooth inclined hill. It climbs the hill with constant velocity. v1=v1x^+v1y^j = (44.2 m/s)^i + (3.23 m/s)^jWhat is the expression in cartesian unit vector notation, for average acceleration of the car during the given time period using the symbols provided?