A particle is traveling in a circular path of radius 3 m. The particle starts at 0 = 0 at t = 0 and has a constant speed of 2 m/s. (a) Where is the particle at t = 2 s? (b) What is the acceleration of the particle at t = = 2 s².?

queston: A particle moves in the x-y plane with an x-component of velocity in meter per second given by vx = 4√t, with t in seconds. The acceleration of the particle in the y-direction in meter per second squared is given by by ay = 4 e(t), with t in seconds. When t-4, y=10, x=4, and vy = 10, (a) Find the equation of the path of the particle and (b) calculate the magnitude of the velocity v of the particle for the instant when its y-coordinate reaches 20 m, and the angle which the velocity makes with the x-axis.

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At t = 0 a truck starts from rest at x = 0 and speeds up in thepositive x-direction on a straight road with acceleration aT. At the sametime, t = 0, a car is at x = 0 and traveling in the positive x-direction withspeed vC. The car has a constant negative x-acceleration: acarx = -aC,where aC is a positive quantity. (a) At what time does the truck pass thecar? (b) At what x-coordinate does the truck pass the car?

A particle hanging from a spring moves with an acceleration that is proportional to itsposition and has the opposite sign. Suppose that a(x) = -4x m/s2 and that the velocity of theparticle is 2 m/s upward when it passes through the origin.a) Determine the velocity of the particle as a fuction of position.b) If the particle is at the origin at t = 1 s, determine its position, velocity andacceleration as a function of time.

A particle is on a circular path as shown in the figure. At position shown, the particle has a speed v = 5 m/s, which is increasing at a rate of 7.5 m/s². What is the magnitude of its acceleration for the same position? v = 5 m/s 2.5 m O a = 10 m/s² O a = 5 m/s² O a 12.5 m/s² O a = 7.5 m/s²

A bird is flying along the straight-line path x = 2t + 7, y =1 - 2,z = 1 – 31, where t is measured in minutes. (a) Where is the bird initially (at i = 0)? Where is the bird 3 minutes later? (b) Give a vector that is parallel to the bird's path. (c) When does the bird reach the point ( )? (d) Does the bird reach (17, 4, -14)?

Starting from rest, a particle moving in a straight line has an acceleration of a = (bt+c) where b = 2 m/s³ and c = - 6m / (s ^ 2) . what is the particle's velocity at 6s and what is its position at 11s?

(b) A particle P is travelling in the positive direction of the x-axis with acceleration kv?, where k is a positive constant and v its speed. At time t =0, it passes through the origin with speed gT and acceleration g. Show that dv dx gT² Hence, obtain an expression for v in terms x, g and T. Prove that at timet, g7*in) Question 4: (a) (i) State the Principle of Moment (Varignon's Theorem). (ii) Prove that the moment of a couple is the same about any axis perpendicular to the plane of action of the couple. (b) A uniform rod Whose centre of gravity G divides it into the ratio AG : GB = a : b is in limiting equilibrium at an angle a with the horizontal with its upper end B resting against a smooth peg and its lower end A attached to a light cord, which is fastened to a point C on the same level as B. Prove that the angle B at which the cord is inclined to the horizontal is given by the equation a+b tanß = b tana + -cot a a

A ball (shown in red color) is constrained to move in a circular path and it is also force to move downwards by the slider (shown in blue color) at a constant velocity of 0.5 m/s. Find the magnitude of acceleration of the ball at the instant when 0 = 60°. Show all necessary diagrams. Slider 2 m 0.5 m/s