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- Problem 2: A baseball is thrown with velocity vo at an angle 0 = 45° above the horizontal. The vertical component of the initial velocity is vo.y = 12.25 m/s. Use a Cartesian coordinate system with the origin at the baseball's initial position.The acceleration of a particle is given by a 4t - 37, where a is in meters per second squared and tis in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t = O is so = 9 m, and the initial velocity is vo = 0 m/s. After you have the general expressions, evaluate these expressions at the indicated times. Answers: m, v m/s Att- 2.9s. m. v- m/s Att 10.6 s, S-Given, position vector of a particle, r(t) = 2t i. Which of the following statements is/are true? All of the above. Magnitude of acceleration is linearly proportional to t. The speed of the particle varies with the time linearly. Direction of velocity changes with the O time but direction of acceleration does not change with the time.
- A particle P is moving along the x-axis. At time t seconds the velocity of the particle is given by the equation v(t) = es and it's initial condition is x(0) = 5m a) Express displacement as a function of time (t) - b) Find the co-ordinates of the particle after 3 seconds.Itourist throws a rock horizontally off the edge of a high cliff, with an initial velocity of lo m.s! a) Taking the y-axis to be upward, write equa- tions for the x- and y. coordinates as functions of time. b) Calculate the values of x and y at times t=0, 0.5, 1.0, 1.5 and 2.0 S c) Write equations for the x and y components of the rock's velocity. d) Find the magnitude and direction of the velocity at time to los. Is the velocity tangent to the trajectory?1つ7 3. An object undergoes motion in 2 dimensions under a constant acceleration of "-2.50 m/s at an angle of 50.0° with respect to the + x direction. It also has an initial velocity of vi = 7.00 m/s at an angle of 10,0° The object begins at the coordinates (0, 0). a) What are the coordinates of the object at t = 7.00 s? Want Cx, y) at t =?4 4tzテメ0チ=XT vse this Con Vxi = \V;l cos v +ハ Ay=lalsin Ga b) What is its total velocity vector of the object as a magnitude and direction at t = 7.00 s? a) Ov= Ton
- the velocity lf the particle changes from -8 fps to 58 fps during 14 sec interval dur8ng which iy acceleration increases unfiromly with the time from an initial value of 3 fps². Determine the displacement covered in the 14s interval. Draw v-t and s-t diagram.1. A particle travels counterclockwise around a circle of 36m radius so that the distance from a fixed point 0 on the right end of a horizontal diameter is given by s=20t + 2t2where s is in meters and t is in seconds. Compute the rectangular components of acceleration at the end of 2 seconds. 2. The particle has an initial velocity of 88mps up to the right at a slope of 4/3. The rectangular components of acceleration are constant at ax=-4m/s2 and ay=-20m/s2. Compute the radius of curvature at the start and at the top of the path.The acceleration of a particle is given by a 3t-37, where a is in meters per second squared and tis in seconds. Determine the velocity and displacement as functions of time. The initial displacement at t=0 is so-8 m. and the initial velocity is vo-2 m/s. After you have the general expressions, evaluate these expressions at the indicated times. Answers: Att 5.5 s. 5 Att-10.5s, 5= m. v L m, m/s m/s
- Problem 3: Aparticle travels in a circular orbit of radius r = 148.7 m. Its speed is changing at a rate of a, = 13.5 m/s² at an instant when its speed is v = 49.8 m/s.The position of a particle that moves along the x-axis is given by: x= t3-3t2-45t (meters) The time t is in seconds. Determine the position (meters), velocity (m/s), and acceleration (m/s2) at t = 8 seconds. Show all necessary math and include all units.Sammy the sugar glider is out one morning foraging for fruit. He waddles his body along a tree branch 4.2m at 30degrees EoN and then turns and leaps and glides to a nearby tree that is 6.5m at 15degrees NoW. Using the triangle method, what was his overall displacement?