At time t = 14 s, the velocity of a particle moving in the x-y plane is v = 0.06i + 2.21j m/s. By time t = 14.05 s, its velocity has become -0.08i + 2.10j m/s. Determine the magnitude day of its average acceleration during this interval and the angle 8 made by the average acceleration with the positive x-axis. The angle is measured counterclockwise from the positive x-axis. Answers: dav = 0 = 3.5608 i 38.15 m/s2
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- A particle initially located at the origin has an acceleration of a = 1.00ĵ m/s2 and an initial velocity of ₁ = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). tî + t²ĵ) m (b) Find the velocity of the particle at any time t. Î+ tĵ) m/s (c) Find the coordinates of the particle at t = 4.00 s. X = y = m m (d) Find the speed of the particle at t = 4.00 s. m/sThe position of a particle moving in the xy -plane is given by 7(t) = (3t2 – t³)î + (t*)j + (- 6t)k. What is the average acceleration of the particle over the time interval between t = 1 s and t = 2 s?A particle moves in the x-y plane with a y-component of velocity in feet per second given by vy = 5.5t with t in seconds. The acceleration of the particle in the x-direction in feet per second squared is given by ax = 3.3t with t in seconds. When t = 0, y = 3.5 ft, x = 0, and vx = 0. The equation of the path of the particle can be written in the form (y - b)³ = cx². Find the constants b and c and calculate the magnitude of the velocity v of the particle for the instant when its x-coordinate reaches 17.4 ft. Answer: b= C = i i When x = 17.4 ft, v = i ft ft ft/sec
- On a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x direction of ax = 3.41 m/s^2, while the other produces an acceleration in the y direction of ay = 7.34 m/s^2. At the end of the firing period, the craft has velocity components of vx = 1860 m/s and vy = 4290 m/s. Find the (a) magnitude and (b) direction of the initial velocity. Express the direction as an angle with respect to the +x axis.At t = 0, a stone is thrown at an angle of 35.0 ◦ above the horizontal with an initial speed equal to 25.0 ms−1. Calculate the magnitudes of the horizontal and vertical components of its displacement at t = 1.20 s.The position of a particle is r(t) = (5.0t2î – 4.0j + 6.0t³k) m. (a) What is the velocity of the particle at 0 s and at 1.0 s (in m/s)? (Express your answers in vector form.) v(0 s) m/s v(1.0 s) m/s (b) What is the average velocity between 0 s and 1.0 s (in m/s)? (Express your answer in vector form.) Vavg m/s
- At t = 0 a particle at the origin has a velocity of 15.1 m/s at 36° above the horizontal x axis. At t = 5.00 s it is at x = 21.0 m and y = 35.0 m and its velocity is 30.0 m/s at 53° above the horizontal. Find: (a) its average velocity; (b) its average accelerationAn object moves on xy plane according to the equation 7 = 20 cos(3t) î + (1,5t + 3,5t2)j. Determine its position at t = 0. Find its average velocity and average acceleration between t = 2s and t = 5s.Problem 2: An object is thrown off the top of a 38-m tall building with a velocity of 350 m/s at an angle of 8.2° with respect to the horizontal. Part (a) How long is the object in the air in seconds? Numeric : A numeric value is expected and not an expression. t = Part (b) What is the maximum height the object reaches above the ground in meters? Numeric : A numeric value is expected and not an expression. hmax = Part (c) What is the horizontal distance the object covers in meters? Numeric : A numeric value is expected and not an expression. Ax =.
- The position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number UnitsThe x-coordinate of a particle in curvilinear motion is given by x= 2.1t³ -2.4t where x is in feet and t is in seconds. The y-component of acceleration in feet per second squared is given by ay = 2.0t. If the particle has y-components y = 0 and vy= 2.2 ft/sec when t = 0, find the magnitudes of the velocity v and acceleration a when t = 2.7 sec. Sketch the path for the first 2.7 seconds of motion, and show the velocity and acceleration vectors for t = 2.7 sec. Answers: V = i a= i ft/sec ft/sec²An object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.