A particle leaves the origin with an initial velocity 3.00î m/s and a constant acceleration a -1.00î – 0.50 m/s². When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?
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- A ball is shot from the ground into the air. At a height of 9.4 m, its velocity is = 7.71+ 6.27 m/s, with i horizontal and upward. (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??Suppose that the position vector for a particle is given as a function of time by (t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.05 m, c = 0.117 m/s2, and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.85 s. = m/s (b) Determine the velocity at t = 2.05 s. = m/s Determine the speed at t = 2.05 s. m/s
- A snowmobile is originally at the point with position vector 26.1 m at 95.0° counterclockwise from the x axis, moving with velocity 4.53 m/s at 40.0°. It moves with constant acceleration 1.83 m/s² at 200°. After 5.00 s have elapsed, find the following. (a) its velocity vector m/s (b) its position vector r = mPlease asapSuppose the position vector for a particle is given as a function of time by , with x(t) = at + b and y(t) =ct2 + d, where a = 1.00 m/s, b = 1.00 m, c= 0.125 m/s2, and d = 1.00 m. (a) Calculate the average velocity during the time interval from t = 1.00 s to t = 4.00 s. (b) Determine the velocity and the speed at t = 3.00 s. (c) Determine the acceleration at t = 3.00 s.
- A proton initially has 7 = (-7.10)î + (5.10)Ƒ + (−6.60)î : and then 2.70 s later has 7 = (4.70)î + (5.10)ĵ + (13.0)ê (in avg meters per second). (a) For that 2.70 s, what is the proton's average acceleration a in unit vector notation, (b) in magnitude, and the angle between a and the positive direction of the x axis? avg (a) Number i 11.8 (b) Number i (c) Number i î+ Units Units i 19.6 k Units m/sSuppose that a dove is flying so that its acceleration vector at time t is given by a(t)=<t^4, t^3, t^2>, its initial velocity is v(0)=<1,2,3> and its initial displacement is s(0)=<7,6,5>. Find the position vector s(t) at time t.A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.) (a) its velocity vector. (b) its position vector.
- Number An ion's position vector is initially 7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s? )ĵ i 1 + = 9.1 m )i + (−9.9 m )ĵ + (−10 m )k, ) + (-10 m ), and 6.7 s later it is -0.37313433 Ĵ + MI -2.46268657 k Units m/sA particle initially located at the origin has an acceleration of a = 2.00ĵ m/s² and an initial velocity of = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( tî + (²ĵ) m f (b) Find the velocity of the particle at any time t. ( î+ tj) m/s (c) Find the coordinates of the particle at t = 7.00 s. X = y = m m (d) Find the speed of the particle at t = 7.00 s. m/s Submit AnswerGiven the position vector ~r(t) = t^2ˆi+tˆj in meters, what is the magnitudeof the velocity vector at a time of three seconds?