The position co-ordinates of a particle movingin a 3-D coordinate system is given byx = a costy = a sintand z = atThe speed of the particle

The coordinates of a moving particle at time t are given by x=ct2 and y=bt2. The speed of the particle is given by

2. A particle moving in the xy-plane has position (𝑥(𝑡),𝑦(𝑡)) at time 𝑡≥0, where  𝑑𝑥𝑑𝑡=cos(𝑡2) and 𝑑𝑦𝑑𝑡=𝑒𝑡sin(𝑡2). At time 𝑡=0, the particle is at position (1,2). The figure above shows the path of the particle for 0≤𝑡≤2.(a) Find the position of the particle at time 𝑡=2.

The position of a particle moving along the x-axis is given by x = a (t – 1) + b(t – 1) where a and b are constant, then :

A particle is moving in the xy-plane has velocity components  dxdt=2t𝑑𝑥𝑑𝑡=2𝑡 and  dydt=4.𝑑𝑦𝑑𝑡=4. If the particle starts from the origin at t = 0, magnitude of its displacement at t = 2 s isOnly one correct answerA.

The position vector of a particle as afunction of time is given by :ˆ ˆ( ) 8 cos 3 8 sin 3r t t i t j→= +Determine its velocity and acceleration.Show that both its speed and themagnitude of its acceleration are constant.