A particle moves in a parabolic path y = cx? with a constant speed vo. Find expressions for the velocity v and acceleration a of the particle when it is at position (x, y). vo Vi+4c²x² (î + 2cxĵ) a = 2cv? (1+4c²x²)² :(-2cxî + j) v = ANS
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- A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)A truck travels around a circular track. The position of the truck is described by the equations (400 · cos 0) m and 0 = (0.002 · t) rad, where t is in seconds. r = r = f@) Using cylindrical coordinates, a. Determine the truck's radial and transverse components of velocity at t = 4 s, v, and vo. b. Determine the truck's radial and transverse components of acceleration at t = 4 s, a, and ag.A particle of mass m has a time-dependent position vector r(t) = (Rcos(ωt),Rsin(ωt),αt) in Cartesian coordinates, where R, ω and α are positive constants. What are the physical dimensions of R, ω and α? Show that the speed of the particle is constant. Does it mean that the acceleration is zero? Justify.
- 3.1How would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)at an instant in time a particles velocity is v = (2.00i + 1.00j) m/s, while it’s acceleration is a = -1.00i m/s^2. at what rate is the particle speeding up / slowing down and what’s the radius of the curve on the particles trajectory
- The velocity of a particle as a function of time is given by v(t)=(3t-t )i-4 j all in S.I. units. a) What are the dimensions of the "-1 " in the – ti term? What are the units of the "3 " in the 3t i term? b) Find the position vector of the particle, r(t), if r(0) = -5 i- 2j :) Find the time ti > 0 when the position in the i direction is a maximum. d) Find a 1 -> 3 the average acceleration vector in the time interval 1 to 3 seconds.The velocity vector of a particle is given by: V = Vje-)[sin(wt)i + cos(wt)j] where, Vo = 12.1 m/s; T = 2.5 s; w = 5.2 rad/s Calculate the magnitude of the acceleration (in m/s2) at t = 7.4 s