The position of a particle moving along an x axis is given byx- 12 n - 2.00r, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t= 4.00 s
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- Using SI base units, a particle’s position as a function of time is given by x(t)=(7t3+4t2+6) m. (a) At what time will the particle’s acceleration be zero? (b) Find the speed of the particle at that time.An object is initially moving in the x-direction at 2.9 m/s when it undergoes acceleration in the y-direction for a period of 14 s. If the object moves equal distances in the x- and y-directions during this time, what’s the magnitude of its acceleration?A particle is undergoing a uniform rectilinear motion and the displacement as a function of time is given by r(t) = 6t4- 2t3 -12t2+3t+3 where r is in meters and t is in seconds. What is a uniform motion? Find the average velocity of the particle between t = 0 and t = 2s When is the acceleration zero?
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- If the car’s speed decreases at a constant rate from 70 mi/hmi/h to 40 mi/hmi/h in 3.0 ss, what is the magnitude of its acceleration, assuming that it continues to move in a straight line? What distance does the car travel during the braking period?In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax(t) = 8t - 2t2 + 15e-t/F, where t is in seconds, ax is in meters per square second, and the constant F is in seconds. At t = 0, the particle was at position x = 3 m with a velocity pointing towards the positive x-axis and having magnitude 25 m/s. In the following problem you can take the constant F = 1.0 s.A particle experiences a constant acceleration, α. At t = T, the particle’s position and speed are observed to be x(t = T) = β and v(t = T) = γ (with the appropriate units), respectively. Find the following quantities in terms of the given quantities (i.e., α, β, γ, and T), i) the initial speed,ii) the initial position,iii) the speed as a function of time, and iv) the position as a function of time.
- At t=0 an object starts from the origin and moves with a constant acceleration of a→=(−3.2i−2.7j)m/s2 on a horizontal surface. If the initial velocity of the object is vo→=(14.1i−18.3j)m/s, determine the magnitude of velocity at t=2.1s. Express your answer in units of m/sm/s using zero decimal places.On a spacecraft two engines fire for a time of 567 s. One gives the craft an acceleration in the x direction of ax = 4.80 m/s2, while the other produces an acceleration in the y direction of ay = 7.52 m/s2. At the end of the firing period, the craft has velocity components of vx = 3751 m/s and vy = 4834 m/s. Calculate the magnitude of the initial velocity.The position of a particle moving along the x axis is given by x = (10 +5t -4.0t2)m, where t is in s. What is the average velocity (in m/s) during the time interval t= 1.0s to t =2.0s