The position of a particle moving along the x-axis is given by x(t) = t^3 +...

The position of a particle moving along the x-axis is given by x(t) = t^3 + 9t^2 − 21t with t is in [0, 2]. (a) Find the velocity and acceleration of the particle.

(b) For what t-values is the velocity 0? (Enter your answers as a comma-separated list.)

(c) When is the particle moving to the left (velocity is negative)? (Enter your answer using interval notation.)

When is the particle moving to the right (velocity is positive)? (Enter your answer using interval notation.) (

d) What is the farthest the particle gets to the left? What is the farthest the particle gets to the right?

(e) When is the velocity increasing? (Enter your answer using interval notation. If an answer does not exist, enter DNE.) When is the velocity decreasing? (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

(f) What is the maximum velocity of the particle? v =

Expert Solution

milcah answered 2 years ago

The position of a particle moving along the x axis is given in centimeters by x...

The position of a particle moving along the x axis is given in centimeters by x = 9.72 + 1.85 t3, 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...

The position of a particle moving along an x axis is given by x = 12.0t2...

The position of a particle moving along an x axis is given by x = 12.0t2 - 4.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 5.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at...

The position of a particle moving along an x axis is given by x = 16.0t2...

The position of a particle moving along an x axis is given by x = 16.0t2 - 6.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 3.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at...

he position of a particle moving along an x axis is given by x = 13.0t2...

he position of a particle moving along an x axis is given by x = 13.0t2 - 3.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 7.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at...

Particle Position and Time The position of a particle moving along the x axis depends on...

Particle Position and Time The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. (a) What dimension and units must c have? s2/ms/m2 m/s2m2/s What dimension and units must b have? m3/ss/m3 s3/mm/s3 For the following, let the numerical values of c and b be 3.3 and 1.0 respectively. (b) At what time does the particle reach its maximum positive...

The position of a particle moving along the x axis depends on the time according to...

The position of a particle moving along the x axis depends on the time according to the equation x = ct2 - bt3, where x is in meters and t in seconds. For the following, let the numerical values of a and b be 3.7 and 1.0 respectively. a) At what time does the particle reach its maximum positive x position? b) What distance does the particle cover in the first 4.0s? c) What is its displacement from t=0s to...

A particle moves along the x axis. It is initially at the position 0.250 m, moving...

A particle moves along the x axis. It is initially at the position 0.250 m, moving with velocity 0.070 m/s and acceleration -0.250 m/s2. Suppose it moves with constant acceleration for 3.90 s. Assume it moves with simple harmonic motion for 3.90 s and x = 0 is its equilibrium position. (a) Find its position. (b) Find its velocity at the end of this time interval.

A particle moves along the x axis. It is initially at the position 0.200 m, moving...

A particle moves along the x axis. It is initially at the position 0.200 m, moving with velocity 0.140 m/s and acceleration -0.410 m/s2. Suppose it moves with constant acceleration for 5.50 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 5.50 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you...

The position of an object moving along an x axis is given by x = 3.12...

The position of an object moving along an x axis is given by x = 3.12 t - 4.08 t2 + 1.10 t3, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object's displacement between t = 0 and t = 4 s? (f) What is its average velocity from t...

2). A particle moving on the x-axis has a time-dependent position (t) given by the equation...

2). A particle moving on the x-axis has a time-dependent position (t) given by the equation x (t) = ct - bt^3. Where the units of x are meters (m) and time t in seconds (s). (Hint: you must get derivatives, you need graph paper) (a) So that the position in x has units of meter which are the units of the constants c and b? If c = 5 and b = 1. From ti = 0s to tf...

Question