Question

In: Math

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.

Expert Solution

(Acceleration )

(Because )

(as given particle at rest initially v(0)=0)

(velocity )

(Given x(1)=3)

milcah answered 2 years ago

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...

Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to...

Suppose a particle moves along the x-axis beginning at 0. It moves one integer step to the left or right with equal probability. a)What is the pdf of its position after three steps? b)What is the pdf of its position after three steps if the x-axis beginning at 1? c)What is the pdf of its position after two steps? d)What is the pdf of its position after two steps if the x-axis beginning at 1?

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...

A particle of mass ? moves in one dimension along the ?- axis. Its potential energy...

A particle of mass ? moves in one dimension along the ?- axis. Its potential energy is given by ?(?) = ??3 − ??, where ? and ? are positive constants. (a) Calculate the force on the particle, ?(?). Find the position of all equilibrium points and identify them as stable or unstable. (b) Draw an energy diagram showing the potential energy U, the kinetic energy K, and the total mechanical energy E for bound motion. Show the location of...

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t...

A 0.150 kg particle moves along an x axis according to x(t) = −13.00 + 2.00t + 3.50t2 − 2.50t3, with x in meters and t in seconds. In unit-vector notation, what is the net force acting on the particle at t = 3.55 s? F with arrow = ______ N

A car moves along an x axis through a distance of 980 m, starting at rest...

A car moves along an x axis through a distance of 980 m, starting at rest (at x = 0) and ending at rest (at x = 980 m). Through the first 1/4 of that distance, its acceleration is +3.00 m/s2. Through the next 3/4 of that distance, its acceleration is -1.00 m/s2. What are (a) its travel time through the 980 m and (b) its maximum speed?

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b...

Particle A moves along an axis in the laboratory with velocity V = 0.3c. Particle b moves with velocity of V = .9c along the direction of motion of particle A. What kinetic energy does the particle b measure for the particle A?

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 3kg particle moves along the X axis according to X(t) = 6t+3t2+2t3, where X is...

A 3kg particle moves along the X axis according to X(t) = 6t+3t2+2t3, where X is in meters and t is in seconds. What net force is acting on it at t = 3 s?