Solved Example & Practice Problems: Rectangular Components

Curvilinear Motion (Rectangular Components)

Solved Examples for Understanding

Example 9.6.1 

The motion of particles A and B is defined by their position vectors where t is in seconds. Determine the point where the particles collide and their speeds just before collision. At what time do they collide ?

Solution: 

The two particles collide when

Time is not negative and the common solution for the two equations is t= 2 seconds. 

⸫ The point where they collide is (10, 25).

Example 9.6.2 

A particle moves along the path y = 4x2 + 8x + 10 starting with an initial velocity If vx is constant, determine vy, and ay at x = 3 m.

Solution: 

Given

Again differentiate w.r.t. 't'

Substituting the values in equation (1) and (2),

Example 9.6.3

The Y-co-ordinate of a particle maving along a curve is y = t3 - 61 + 3 where y is in metres and t in seconds. Its acceleration in x-direction is given by ax = 4t +3 m/s2. If velocity of the particle in x direction is 2 m/s when t = 0, calculate the magnitude and direction of velocity and acceleration of the particle when t = 1s.

Solution :

Example 9.6.4 

The velocity of a particle moving in x-y plane is given by m/s at t = 2 s. Its average acceleration during the next Determine the velocity at t = 4 s and the angle between the average acceleration vector and the velocity vector at t = 4s?

Solution :

Angle between average acceleration vector and velocity vector at t = 4 s = 63.43 - 21.8 = 41.63°.

Examples for Practice

Q.1

The velocity of a particle moving in the x-y plane is given by 6.12 î + 3.24 ĵ ↑ m/s at time t = 3.65 s. Its average acceleration during the next 0.02s is 4 î + 6 ĵ ↑ m/s2. Determine the velocity vector of the particle at t = 3.67 s and the angle θ between the average acceleration vector and velocity vector at t = 3.67 s.

[Ans. : = 6.2 î + 3.36 ĵ, θ = 27.85°]

Q.2

A particle moves in a curved path so that ax = 40 - 12t m/s2 and y = t3 m, where t is in seconds. If the particle starts from rest, at the origin, determine velocity of the particle at t = 2 s.

[Ans. : v = 57.27 m/s, 12.1° ]