Concept explainers
A particle initially located at the origin has an acceleration of
(a)
The vector position of the particle at time
Answer to Problem 3P
The vector position of the particle at time
Explanation of Solution
Write the expression for the vector position of the particle.
Here,
Conclusion:
Substitute
Therefore, the vector position of the particle at time
(b)
The velocity of the particle at any time
Answer to Problem 3P
The velocity of the particle at any time
Explanation of Solution
Write the expression for the velocity of the particle at any time
Here,
Conclusion:
Substitute
Therefore, the velocity of the particle at any time
(c)
The coordinates of the particle at
Answer to Problem 3P
The coordinates of the particle at
Explanation of Solution
Write the expression for the vector position of the particle at time
Here,
Conclusion:
Substitute
So compare the above value with (III) to get
Therefore, the coordinates of the particle at
(d)
The speed of the particle at
Answer to Problem 3P
The speed of the particle at
Explanation of Solution
Write the expression for the speed of the particle at time
Write the final speed of the particle.
Here,
Conclusion:
Substitute
Substitute
Therefore, the speed of the particle at
Want to see more full solutions like this?
Chapter 3 Solutions
Principles of Physics: A Calculus-Based Text
- At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi=(3.00i2.00j)m/s and is at the origin. At t = 3.00 s, the particles velocity is vf=(9.00i+7.00j)m/s. Find (a) the acceleration of the particle and (b) its coordinates at any time t.arrow_forwardA particle initially located at the origin has an acceleration of a = 1.00ĵ m/s2 and an initial velocity of ₁ = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t²ĵ) m (b) Find the velocity of the particle at any time t. Î+ tĵ) m/s (c) Find the coordinates of the particle at t = 4.00 s. X = y = m m (d) Find the speed of the particle at t = 4.00 s. m/sarrow_forwardA particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 9.00 s.x = my = m(d) Find the speed of the particle at t = 9.00 s. m/sarrow_forward
- Let the position vector (with its tail at the origin) of a moving particle be~r(t) = t^(2)ˆi − 2tˆj + (t^(2) + 2t)ˆk, where ~r(t) is measured in meters and t is measured in seconds.(a) Find the acceleration vector and the magnitude of the particle at time t.(b) Find the acceleration vector and the magnitude of the particle when it passes throughthe point (4, -4, 8).arrow_forwardThe acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at the origin at t = 0 s and has an initial velocity Vo = 2(m/s) i + 3(m/s) j. Find: a) The velocity of the particle as a function of time. b) The maximum height the particle reaches.arrow_forwardFrom the origin, a particle starts at t = 0 s with a velocity vecv=7.0hatim//s and moves in the xy plane with a constant acceleration of veca=(-9.0hati+3.0hatj)m//s^(2). At the time the particle reaches the maximum x coordinate, what is its (a) velocity and (b) position vector?arrow_forward
- A particle initially located at the origin has an acceleration of = 4.00ĵ m/s2 and an initial velocity of i = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 7.00 s.x = my = m(d) Find the speed of the particle at t = 7.00 s.m/sarrow_forwardThe velocity of a particle moving in thex-y plane is given by (4.03i + 7.36j) m/s at time t = 3.64 s. Its average acceleration during the next 0.020 s is (2.2i + 2.6j) m/s?. Determine the velocity v of the particle at t = 3.660 s and the angle e between the average- acceleration vector and the velocity vector at t = 3.660 s. Answers: v= ( i i+ i j) m/s e =arrow_forwardThe acceleration of a particle is a = (5.00 i - 7.00 j) m/s^2. At t = 0, the particle leavesthe origin with an initial velocity v0 = (4.00 i + 1.00 j) m/s. (a) What is the y-coordinate of the particle when its x-coordinate reaches 2.00 m? (b) What are the magnitude and direction of the particle's velocity when its x-coordinate reaches 2.00 m? Draw this velocity vector.arrow_forward
- A particle initially located at the origin has an acceleration of a = 1.00j m/s2 and an initial velocity of v; = 6.00î m/s. %3D (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t2 j) m (b) Find the velocity of the particle at any time t. tj) m/s (c) Find the coordinates of the particle at t = 7.00 s. X = m y = m (d) Find the speed of the particle at t = 7.00 s.arrow_forwardA 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 sarrow_forwardA 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 Answerarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning