What is the average velocity at a specific time t = t0 and t = t1 of a particle in motion where its position (y) is a real valued function of time (t); that is, y = y(t) ? What is the instantaneous velocity at t = t0? Explain with the example y = t 2 + 2t for t0 = 1 second and t1 = 2, 1.5, 1.1, 1.01 seconds.
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3.) The position of a particle is given by x(t) = 3t3 โ 2t2 โ 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...
Average and Instantaneous Velocity A particle moves along the x axis. Its position varies with time acording to the expression x =-4t + 2t2, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times...
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s=3cos(๐t)+5cos(๐t), where t is measured in seconds. (Round answer to 2 decimal places)(a) Find the average velocity during each time period.(i) [1, 2]: 10 cm/s(ii) [1, 1.1]: __ cm/s(iii) [1, 1.01] __ cm/s(iv) [1, 1.001] __ cm/s(b) Estimaate the instantaneous velocity of the particle when t=1. __ cm/s
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 5 sin ฯt + 2 cos ฯt, where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) [1, 2] ? cm/s (ii) [1, 1.1] ? cm/s (iii) [1, 1.01] ?cm/s (iv) [1, 1.001] ?cm/s (b) Estimate the instantaneous velocity of the particle when...
The position of a particle moving along the x axis is given in centimeters by x = 9.55 + 1.01 t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is...
y/yi PROBLEM 11.93 The damped motion of a vibrating particle is defined by the position vector r +)+2co2,where r is expressed in seconds. For 30 mm and y,-20 min, determine the position, the velocity, and the acceleration of the particle when (a) t0, (b) t-1.5 s. 1.0 0.5 0 0.4 06 t 0.2 -0.5
Problem #1 The motion of a particle is defined as x=t2-8t + 7 and y = 0.5t? + 2t-4 where x and y are in meters and t is in seconds. Determine the following: (a) The magnitude of the smallest velocity reached by the particle (b) The time, position, and direction of that velocity
Problem # 4 (Graded) The motion of a particle is defined as x t2-8t7 and y 0.5t2 +2t 4 where x and y are in meters and t is in seconds. Determine the following: (a) The magnitude of the smallest velocity reached by the particle (b) The time, position, and direction of that velocity.
8. A student rolls a marble alongside a meterstick to measure its velocity. At t1 = -2.5 s, its position is x1 = 4.3 cm, and at t2 = 4.5 s it is at x2 = 18.5 cm. Determine its average velocity during this time interval. 9. The position of a ball rolling along a straight line is given by ? = 1.8โ3.6? +1.5?2, where x is in meters and t is in seconds. Determine the average velocity of the...
3. A particle moves according to the function 3-5t2 4 where 0 is in radians and t is in seconds. (a) Find the angular velocity of the particle at 1 s and t-2 s, (b) Find the average instantaneous acceleration between t-1 and t = 2 s. (c) what is the angular position of the particle at the first time when the angular velocity is 0?