The acceleration of a particle in one dimensional motion at time t is given by at t () 6 2 = − . Given that the initial velocity of the particle is 0, find the average velocity of this particle over the first 4 seconds.
Please solve and show work. Thank you so much!

The acceleration of a particle in one dimensional motion at time t is given by at...
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...
Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations r-|kıBeos(K2O) ] m and θ (k31) rad, where t is expressed in seconds. Please note that ki, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0 when t 0 sec. So, when t 2 sec, Find a) The "script" values for radial...
Dynamics
Given: The motion of a particle P is defined by the relations r = [kı sin(b) m and 0=(k21°) rad, where t is expressed in seconds. Please note that kı, k2, and b are constants which are greater than zero. For the initial condition, the particle has an angle of o=0° when t = 0 sec. So, when 1 = 1 sec, Find: a) The radial (vr) and transverse (ve) components of velocity of the particle P. b) The...
Last Name: Page Problem #2 (35 Points) Given The motion of a particle P which coincides with the robot's gripper hand at point A is defined by the relations where t is expressed in seconds. Please note that kı, k2, and ks are constants which are greater than zero. For the initial condition, the particle has an angle of 0-0° when-0 sec. So, when t 2 sec, Find: a) The "script" values for radial and transverse coordinates, that is, r,t,i,...
Solve please
(2 points) Suppose that the equation of motion for a particle (where s is in meters and t in seconds) is s = 3t3 - 8t (a) Find the velocity and acceleration as functions of t. Velocity at time t = Acceleration at time t = (b) Find the acceleration after 1 second. Acceleration after 1 second: (C) Find the acceleration at the instant when the velocity is 0. Acceleration:
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
Need both answered please!
1. A particle moves with acceleration function a(t) = 8t + 5. Its initial velocity is v(O) = -4 cm/s and its initial displacement is s(0) = 5. Find its position after t seconds. s 2. The equation of motion of a particle is S = t3 - 9t, where s in meters, and t is in seconds. Find a) The velocity and acceleration as a function oft b) The acceleration after 4 seconds.
An object moves in one dimensional motion with constant acceleration a = 6.9 m/s2. At time t = 0 s, the object is at x0 = 1.7 m and has an initial velocity of v0 = 3.6 m/s. How far will the object move before it achieves a velocity of v = 6.2 m/s? Your answer should be accurate to the nearest 0.1 m.
An object moves in one dimensional motion with constant acceleration a = 5.9 m/s2. At time t = 0 s, the object is at x0 = 4.1 m and has an initial velocity of v0 = 4.4 m/s. How far will the object move before it achieves a velocity of v = 8.5 m/s? Your answer should be accurate to the nearest 0.1 m.
An object moves in one dimensional motion with constant acceleration a = 4.8 m/s2. At time t = 0 s, the object is at x0 = 1.4 m and has an initial velocity of v0 = 3.6 m/s. How far will the object move before it achieves a velocity of v = 6.5 m/s? Your answer should be accurate to the nearest 0.1 m.