Chapter 12, Problem 12P

The motion of a particle is defined by the function  x = at3 - bt2 - ct + d  where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?

Specifically a dynamics of a particle question: The acceleration of a particle as it moves along a straight line is given by a = (2t - 1) m/s2. If s = 1 m and v = 2 m/s when t = 0, determine the particle's velocity and position when t = 6 s. Also determine the total distance the particle travels during this time period.

2 The motion of a particle is defined by the relation. x=t²-10t+30 where, X in meters, t in sec. Determine 1 when the velocity is zero. (5 sec) 2 the position and total distance traveled when t≤ 8 sec (x+=8=14m, Distance = 39 m).

A motorcycle travels along a straight line with a velocity [ v = ( 2t² – 8 ) m/s ], where ( t ) is in seconds. When ( t = 1 s ), the motorcycle is located ( 10 m ) to the right of the origin. Determine: a- The displacement from ( t = 0 ) to ( t = 10 s ). b- The distance traveled by the motorcycle for the same time interval. c- The average velocity at this time interval. d- The average speed at this time interval. e- The acceleration at ( t = 5 s ).

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The motorcycle is traveling at 45 m/s when it is at A. The speed is then decreased at v= -(0.05s) m/s², where s is in meters measured from A. Suppose that p = 150 m (Figure 1) Figure P 60° P B 1 of 1 ▼ Part A Determine the speed of the motorcycle when it reaches B. Express your answer to three significant figures and include the appropriate units. UB= Submit Part B a = Part C O 0 = Value Determine the magnitude of the acceleration of the motorcycle when it reaches B. Express your answer to three significant figures and include the appropriate units. μA Submit Request Answer Value Submit Request Answer μA Provide Feedback Units Determine the direction of the acceleration of the motorcycle when it reaches B measured counterclockwise from the negative axis. Express your answer using three significant figures. Units 15. ΑΣΦ ↓↑ vec Request Answer ? ? ? O Next >

The acceleration of a particle is given by a = 5t - 19, where a is in meters per second squared and t is in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = 0 is so = -6 m, and the initial velocity is vo = 7 m/s. Once you have determined the functions of time, answer the questions. Questions: When t = 4.6 s, %3D S = m V = m/s m/s? =

topic:  Rectilinear Motion & Plane Curvilinear Motion

Each of four particles move along the x-axis. Their positions (in meters) as functions of time (in seconds) are given as follows: Particle 1: (t) = 3.5 - 2.7³ Particle 2: (t) = 3.5+ 2.7+³ Particle 3: x (t) = 3.5 - 2.7² Particle 4: x (t) = 3.5-3.4t - 2.7t² Which of these particles have constant acceleration? O Only 1 and 2 Only 3 and 4 None of them Only 2 and 3 O All of them