Concept explainers
(a)
The velocity as the function of time for the given time interval.
(a)
Answer to Problem 111P
The velocity as the function of time interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for the acceleration of the particle.
Here,
Substitute
Simplify above expression.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the velocity as the function of time interval is
(b)
The position as function of time for the given time interval.
(b)
Answer to Problem 111P
The position as function of time for the given interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for the velocity of the particle as function of time for given time period.
Write expression for velocity of the particle.
Here,
Rearrange above expression for
Calculation:
Substitute
Simplify above expression.
........(3)
Substitute
Substitute
Substitute
Conclusion:
Thus, the position as function of time for the given interval is
(c)
The average velocity for the given time interval and compare to the average of instantaneous velocities of starting and ending times.
(c)
Answer to Problem 111P
The average velocity for the given time interval is
Explanation of Solution
Given:
The acceleration of the particle is given by
The velocity of particle at
The position of particle at
Formula used:
Write expression for average velocity of the particle.
Write expression for instantaneous velocity of the particle.
........(5)
Write expression for average of instantaneous velocities for
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the average velocity for the given time interval is
Want to see more full solutions like this?
Chapter 2 Solutions
Physics for Scientists and Engineers
- V, is the velocity of a particle moving along the x axis as shown. (a) If x = -2.0 m at 1 = 0.0 s, what are the positions of the particle at 1 = 1.0 s and 6.0 s? (b) What is the average velocity of the particle during the time interval t=0.0 s to t= 6.0 s? (c) What is the average acceleration of the particle during the time interval t=0.0 s to t= 6.0 s? (d) What are the acceleration of the particle at i = 1.0 s, 3.0 s and 6.0 s?arrow_forwardA particle moves in a straight line and has acceleration given by a(t)=2t−2 m/s2 . Its initial velocity is v(0)=−3 m/s and its initial displacement is s(0)=−2 m . Find its position function s(t) .arrow_forwardA particle moves along the x axis. It is initially at the position 0.330 m, moving with velocity 0.250 m/s and acceleration -0.330 m/s?. Suppose it moves with constant acceleration for 3.40 s. (a) Find the position of the particle after this time. m (b) Find its velocity at the end of this time interval. m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.40 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. (e) Find its phase constant o, if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one…arrow_forward
- Suppose that the acceleration of a particle as it moves along a straight line is constant at 8 mm/s2 where ss refers to seconds. (a) Let v(t) be the velocity of the particle at time t=0. If the particle starts with an initial velocity of 20 mm/s, determine the particles velocity at time t=10. (b) Let d(t) be the distance the particle has travelled from its origin at time 0 to where it is at time t. Determine the distance the particle has travelled at time t=10.arrow_forwardAt t = 10 s, a particle is moving from left to right with a speed of 5.0 m/s. At t = 20 s, the particle is moving right to left with a speed of 8.0 m/s. Assuming the particle’s acceleration is constant, determine (a) its acceleration, (b) its velocity at time t = 0, and (c) the instant when its velocity is zero.arrow_forwardThe velocity of a particle at any time t moving along an x-axis is given by the following equation: v = 3t - 8t + 3 where v is in m/s. At t = 0, x = 0. Determine the following: (a) the particle's displacement between t = 0 and t = 4 s (b) the average velocity for the time interval t =0 to t = 4 s (c) the acceleration when t =3 s (d) the instantaneous velovity at t = 4 s (e) what is the initial direction of motion of the particle?arrow_forward
- A particle acceleration is given by a(t) = At2 + Bt − C where A, B, and C are constants. At t = 0, the particle starts its motion at the origin with initial velocity v0. Find the position and speed of the particle as a function of time.arrow_forwardDo the first questionarrow_forwardThe acceleration of a particle is given by ax(t)=−2.00m/s2+(3.00m/s3)t. Find the initial velocity v0x such that the particle will have the same x-coordinate at time t = 4.93 s as it had at t=0.arrow_forward
- Suppose the position vector for a particle is given as a function of time by r(t)=x(t)i^+y(t)j^, with x(t)=at+b and y(t)=ct2+d, where a=1.00m/s,b=1.00m,c=0.125m/s2, and d=1.00m. (a) Calculate the average velocity during the time interval from t=2.00s to t=4.00s. (b) Determine the velocity and the speed at t=2.00sarrow_forwardThe position of a particle moving along the x-axis is given by x(1) = 4.0 – 2.0t m. (a) At what time does the particle cross the origin? (b) What is the displacement of the particle between t = 3.0 s and t = 6.0 s?arrow_forwardThe position of a particle moving along the x-axis is given by x(t) = 3.0 — 1.7t m. (Assume t is in seconds.) (a) At what time (in s) does the particle cross the origin? S (b) What is the displacement (in m) of the particle between t = 3.5 s and t = 7.0 s? (Indicate the direction with the sign of your answer.) marrow_forward
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON