4. (25 pts.) A particle is moving along the x-axis in accordance with the following: x(t)...
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.50cm, and the frequency is 2.30 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) x...
3. A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t=0 s and moves to the right. The amplitude of its motion is 2.00 cm, and the frequency is 1.50 Hz. (a) Determine the position, velocity, and acceleration equations for this particle. (b) Determine the maximum speed of this particle and the first time it reaches this speed after t=0 s.
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is2.50 cm, and the frequency is 1.30 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t, and ?.) x = (b) Determine the maximum speed of the particle. cm/s (c) Determine the earliest time (t...
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t0 and moves to the right. The amplitude of its motion is 2.50 cm, and the frequency is 2.90 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) x2.5sin (5.8xt)...
For timet > 0, the acceleration of a particle moving along the x-axis is given by a (t) = cost+t. At time t = 0, the velocity of the particle is 8 and the position of the particle is 0. What is the position of the particle at time t = ?
The velocity of a particle moving along x-axis is given by v(t) = 4 alpha middot t^2 - beta middot t in m/s. (a) Find the units of measurement of the known constants alpha and beta. (b) Find the average acceleration of the particle during its first 5 s of its motion. (c) When does the particle stop momentarily? (d) How far is the particle from the origin at that instant, if x(t = 0) = 0? (e) Find the...
The position of a particle moving along an x axis is given by x = 12. t2 2.00t3 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 = 4.00 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 = 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 = 6.00 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...
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 2.60 cm, and the frequency is 1.20 Hz (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.)...
The position of a particle moving along an x axis is given by x 14.0t2 - 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 = 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 what...