The position of a particle moving in the xy plane varies with time, and its coordinates are given by the following expressions: x(t) = 4.00 m +r cos[(4.00/s)t] and y(t) = r sin[(4.00/s)t], where r = 2.00 m, and x and y will be in meters when t is in seconds. Determine the following for this particle. (a) speed of the particle at any time m/s (b) magnitude of the acceleration of the particle at any time m/s?

(b) An electron is moving on a detector screen. The electron starts from rest. At 5.0 s, the acceleration of the electron is å = (6.08 – 4.0j) cm/s². Compute the (i) position (in meters and in unit vector notation) of the electron. (ii) velocity (in m/s and in unit vector notation) of the electron.

(c) Find, to the nearest metre, the distance between points P and R. A car is travelling on a straight horizontal road. The velocity of the car, vms ', at time t secondsm it travels past three points, P, Q and R, is modelled by the equation -1 v = at +bt+c, where a, b and c are constants. The car passes P at time t = 0 with velocity 8 ms. (a) State the value of c. The car passes Q at time t = 5 and at that instant its deceleration is 0.12 ms2. The car passes R at time t = 18 with velocity 2.96 ms-1. %3D (b) Determine the values of a and b. (e) Find, to the nearest metre, the distance between points P and R

A projectile is launched from the point (x = 0, y = 0), with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance T from the ori- gin at the end of each second thereafter, for 0 < t s 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v, and v, will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to r, then r must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).

A particle moves along a horizontal path with a velocity of v = (31²-61) m/s, where is the time in seconds. If it is initially located at the origin O, determine the distance traveled in 3.5 s, and the particle's average velocity and average speed during the time interval.

(e) Two boats leave the same port at the same time. One travels at a speed 10 mi/h in the direction S 12° W and the other travels at a speed of 20 mi/h in a direction S 72⁰ W. How far apart are the two boats after one hour?

The velocity of a particle is given by v = {16t’i + 4t°j + (5t + 2)k} m/s, where t is in seconds. If the particle if at the origin when t = 0, determine the z-coordinate position %3D of the particle when t = 2 s.

A projectile launches at an initial velocity of 55 m/s. Determine the length of time it will take the projectile to land. g = 9.81 m/s^2 Vo 30° M N Ad, = (v,)t Ad, - = (v, )t V2y = Vi, - gt (v,) = (v, ) - 2g(Ad,) v = v, cos e (constant) Viy = v, sin e 1 = initial 2 = final

a projectile is fired from the ground with an initial velocity of 250m/s at an angle of 60 degrees above the horizontal