The position of a particle moving along the x axis is given in centimeters by x =9.75 + 1.50t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t =2.00 s and t = 3.00 s. (f) Graph x versus t and indicate your answers graphically.

The position of a particle moving along the x axis is given in centimeters by x =9.75 + 1.50t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t =2.00 s and t = 3.00 s. (f) Graph x versus t and indicate your answers graphically.

Name: The position of a particle moving along the x axis is given in centime
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: The position of a particle moving along the x axis is given in centimeters by x =9.75 + 1.50t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t 2.00 s;

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 6P: The position of a particle moving along the x axis varies in time according to the expression x =...

See similar textbooks

Similar questions

An object moves horizontally according to the equation x = 3t^3 − 5t + 7, where x is meters and t in seconds. (a) Determine the average velocity in the time interval of 2.00 s to 4.00 s. (b) Find the instantaneous velocity at t = 3.60 s. (c) Find the instantaneous acceleration at t = 4.00 s.
A particle moving in 1D has time-dependent velocity which is given by the quadratic function v(t) = At2 + Bt + C, where A = 4.5 m/s3, B = 3.6 m/s2, and C = −1.7 m/s. a) Find the average acceleration of the particle between t = 0 s and 2.5 s. b) Find the average acceleration of the particle between t = 2.5 s and 5.0 s. c) At what time(s) is the particle at rest?
The position of a particle moving along the x-axis varies with time according to x(t) = 5.0t2 − 4.0t3 m. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t = 2.0 s, (c) the time at which the position is a maximum, (d) the time at which the velocity is zero, and (e) the maximum position.
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.
An object’s position is given by x = bt + ct3 , x in meters, t in seconds, b = 1.50 m/s and c = 0.640 m/s3 . To study the limiting process leading to the instantaneous velocity, calculate the object’s average velocity over time intervals from (a) 1.00 s to 3.00 s, (b) 1.50 s to 2.50 s, and (c) 1.95 s to 2.05 s. (d) Find the instantaneous velocity as a function of time by differentiating, and compare its value at 2.00 s with your average velocities.
The velocity of a particle at any time t moving along an x-axis is given by the following equation: v = 3t^2 - 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?
The 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.
An object moves along the x-axis according to the equation ?(t) = (3. 00t3 − 2.00t +1.00) ?. Determine(a) The average speed between t = 2.00 s and t = 3.00 s,(b) The instantaneous speed at t = 2.00 s and at t = 3.00 s,(c) The average acceleration between t = 2.00 s and at t = 3.00 s,(d) The instantaneous acceleration at t = 2.00 s and at t = 3.00 s.
The driver of a car travelling at 65km/h in an easternly direction, steps on the brakes and stops in 4.0s. while braking, the average acceleration of the car in (m/s^2) A) 16.3 m/s^2 towards the west B) 4.5 m/s^2 towards the west C) 4.5 m/s^2 towards the east D) 16.3 m/s^2 towards the east
During the time interval 0 < t < 1, the velocity of an object as a function of time is v = 5 + 3t^2 + 2t^3. Knowing that the object follows a rectilinear trajectory, What is the correct expression for the acceleration?
The velocity of a particle moving along the x-axis varies with time according to v(t) = A + Bt−1 , where A = 2 m/s, B = 0.25 m, and 1.0 s ≤ t ≤ 8.0 s . Determine the acceleration and position of the particle at t = 2.0 s and t = 5.0 s. Assume that x(t = 1 s) = 0 .
The position of a particle moving along the x axis is given by x = (10 +5t -4.0t2)m, where t is in s. What is the average velocity (in m/s) during the time interval t= 1.0s to t =2.0s