3. A particle starts at rest at point O at instant t=0. The particle accelerates with constant tangential acceleration a_t as it travels along the slit in the direction ccw. Determine r, rdot, theta and thetadot as functions of time during the first revolution of the particle in the slit.

At time t = 0, a particle is at rest in the x-y plane at the coordinates (xo, Yo) = (8, 0) in. If the particle is then subjected to the acceleration components ax=0.53 -0.27t in./sec² and ay = 0.13t - 0.04t² in./sec², determine the coordinates of the particle position when t = 6 sec. You might consider plotting the path of the particle during this time period. Answer: (x, y) = (7.82 -0.3715 )in.

3 Problem The velocity of a particle moving in one dimension is given by v(t) = 2+5+³/2 The particle is at position s(1) = 5 at time t = 1. Determine the following: 1. The acceleration of the particle a(t) 2. The position of the particle s(t) that includes the initial condition so.

At time t = 0, a particle is at rest in the x-y plane at the coordinates (xo, Yo) = (4, 0) in. If the particle is then subjected to the acceleration components ax = 0.84 – 0.51t in. /sec² and ay = 0.14t – 0.02t2 in. /sec2, determine the coordinates of the particle position when t = 6 sec. You might consider plotting the path of the particle during this time period. Answer: (x, y) = ( i i Din.

2. The acceleration of a particle is given by a = (6t-3) m/s2, where t is in seconds. Assume the particle moves in a horizontal direction only. It starts at rest when it is located at 2 m to the right of the origin at t = 0 s. Answer the following questions. a. Is acceleration constant over time? Justify your response by explaining why this is relevant to your analysis. Yes Reasoning: No b. What is the velocity of the particle as a function of time? Show your work. Velocity as a function of time C. Where is the particle located at when t = 5 s? Show your work. Magnitude rounded to 3 sig. fig. Units Units Direction (right or left of origin)

A particle in an experimental apparatus has a velocity given by v = k√s, where v is in millimeters per second, the position s is millimeters, and the constant k = 0.36 mm ¹/25-¹1. If the particle has a velocity vo = 6 mm/s at t = 0, determine the particle position, velocity, and acceleration as functions of time. To check your work, evalutate the time t, the positions, and the acceleration a of the particle when the velocity reaches 35 mm/s. Answers: t = i S= i a = i S mm mm/s²

2/40 Particle 1 is subjected to an acceleration a = -kv, particle 2 is subjected to a = -kt, and particle 3 is subjected to a = -ks. All three particles start at the origin s = 0 with an initial velocity vo time t = 0, and the magnitude of k is 0.1 for all three particles (note that the units of k vary from case to case). Plot the position, velocity, and acceleration ver- sus time for each particle over the range 0 st< 10 s. %3D = 10 m/s at %3D %3D

A particle starts from rest at x = -1.9 m and moves along the x-axis with the velocity history shown. Plot the corresponding acceleration and the displacement histories for the 2.4 seconds. Find the time t when the particle crosses the origin. After you have the plots, answer the questions.

Particle 1 is subjected to an acceleration a = -kv, particle 2 is subjected to a = -kt, and particle 3 is subjected to a = -ks. All three particles start at the origins=0 with an initial velocity vo = 9.8 m/s at time t = 0, and the magnitude of k is 0.19 for all three particles (note that the units of k vary from case to case). Plot the position, velocity, and acceleration versus time for each particle over the range 0≤t≤ 10 s. After you have the plots, answer the questions. Questions: If t = 4.2 s, Particle 1: S= i Particle 2: S= Particle 3: i S= i m, V= i m, V= 3 m, i V= i m/s, a = m/s, i a = i m/s, a = i m/s² m/s² m/s²

At time t = 0, a particle is at rest in the x-y plane at the coordinates (xo, Yo) = (4, O) in. If the particle is then subjected to the acceleration components ax = 0.81 – 0.56t in. /sec2 and ay = 0.14t – 0.02t2 in. /sec?, determine the coordinates of the particle position when t = 6 sec. You might consider plotting the path of the particle during this time period. Answer: (x, y) =( i i Din.