Question

In: Physics

A particle moves in the x-y plane with constant acceleration. At time zero, the particle is...

A particle moves in the x-y plane with constant acceleration. At time zero, the particle is at r = <5.0, 2.0> m and has velocity v = <-4.0, 9.0> m/s. The acceleration is constant and is given by a = <4.0, 6.0> m/s2 . (a) Find the velocity at t = 2.0 s. (b) Find the position at t = 4.0 s. Give the magnitude and direction of this position vector. (c) Sketch (approximately to scale) the vector diagrams for vi , vf , and ?v, and for ri , rf , and ?r

Solutions

Expert Solution

a) Find the velocity at t = 2.0 s.
we have, velocity v = u+at u is the initial velocity,
               so             v = <-4.0, 9.0> + <4.0, 6.0>*2

                                   = <4.0, 21.0> m/s

(b) Find the position at t = 4.0 s. Give the magnitude and direction of this position vector.

                     = r0 + ut + (1/2)at2 = <5.0, 2.0> + <-4.0, 9.0>*4 + (1/2)<4.0, 6.0>*42

                                                        = <21.0, 86.0>

(c) Sketch (approximately to scale) the vector diagrams for vi , vf , and ?v, and for ri , rf , and ?r

genius_generous answered 5 months ago
Next > < Previous

Related Solutions

A particle moves in the xy plane with constant acceleration. At t = 0 the particle...
A particle moves in the xy plane with constant acceleration. At t = 0 the particle is at vector r1 = (3.6 m)i + (2.8 m)j, with velocity vector v1. At t = 3 s, the particle has moved to vector r2 = (11 m)i − (1.8 m)j and its velocity has changed to vector v2 = (4.6 m/s)i − (6.7 m/s)j. (a) Find vector v1. vector v1 = m/s (b) What is the acceleration of the particle? vector a...
A particle moves in the xy plane with constant acceleration. At t = 0 the particle...
A particle moves in the xy plane with constant acceleration. At t = 0 the particle is at r1 = (4.0 m) + (3.0 m), with velocity 1. At t = 3 s, the particle has moved to r2 = (9 m) − (2.0 m) and its velocity has changed to v2 = (5.0 m/s) − (6.0 m/s). i. Find 1 = m/s ii. What is the acceleration of the particle? iii. What is the velocity of the particle as...
A particle, initially at rest, moves along the x-axis so that its acceleration at any time...
A particle, initially at rest, moves along the x-axis so that its acceleration at any time t ≥ 0 is given by a(t) = 12t2−4 . The position of the particle when t=1 is x(1)=3 . Write an expression for the position x(t) of the particle at any time t ≥ 0.
Q.1- At time t=0.00s, a particle located at the origin in the x-y plane has a...
Q.1- At time t=0.00s, a particle located at the origin in the x-y plane has a velocity given by 3.00m/s i + 2.00m/s j. Three seconds later, the velocity is 9.00m/s i - 7.00m/s j. Assume that the particle had a constant acceleration during those three seconds. 1- What was the acceleration of the particle? 2-What is the position of the particle at t=3.00s?
Q3. An object moves with constant acceleration 4.00 m/s2 and over a time interval reaches a...
Q3. An object moves with constant acceleration 4.00 m/s2 and over a time interval reaches a final velocity of 12.0 m/s. (a) If its initial velocity is 6.00 m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its initial velocity is -6.00 m/s, what is its displacement during the time interval? (d) What is the total distance it travels during the interval in part (c)?
An object moves with constant acceleration 3.11 m/s2 and over a time interval reaches a final...
An object moves with constant acceleration 3.11 m/s2 and over a time interval reaches a final velocity of 13.6 m/s. c. If its initial velocity is -5.83 m/s, what is its displacement during the time interval? d. What is the total distance it travels during the interval in part (c)?
An object moves with constant acceleration 4.10 m/s2 and over a time interval reaches a final...
An object moves with constant acceleration 4.10 m/s2 and over a time interval reaches a final velocity of 13.8 m/s. (a) If its original velocity is 6.90 m/s, what is its displacement during the time interval? m (b) What is the distance it travels during this interval? m (c) If its initial velocity is −6.90 m/s, what is its displacement during this interval? m (d) What is the total distance it travels during the interval in part (c)? m
The figure gives the acceleration of a 4.0 kg particle as an applied force moves it...
The figure gives the acceleration of a 4.0 kg particle as an applied force moves it from rest along an x axis from x = 0 to x = 9.0 m. The scale of the figure's vertical axis is set by as = 8.0 m/s2. How much work has the force done on the particle when the particle reaches (a) x = 4.0 m, (b) x = 7.0 m, and (c) x = 9.0 m? What is the particle's speed...
A particle undergoes a constant acceleration of 4.00 m/s2. After a certain amount of time, its...
A particle undergoes a constant acceleration of 4.00 m/s2. After a certain amount of time, its velocity is 12.2 m/s. (Where applicable, indicate the direction with the sign of your answer.) (a) If its initial velocity is 6.1 m/s, what is its displacement during this time? m (b) What distance does it travel during this time? m (c) If its initial velocity is −6.1 m/s, what is its displacement during this time? m (d) What is the total distance the...
A 1.90-kg particle moves in the xy plane with a velocity of v with arrow =...
A 1.90-kg particle moves in the xy plane with a velocity of v with arrow = (4.00 i − 3.70 j) m/s. Determine the angular momentum of the particle about the origin when its position vector is r with arrow = (1.50 i + 2.20 j) m.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT