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.

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.

he displacement of a particle is givenby 𝑥 = (𝑡 − 2)2 where x is in meters andt in seconds. The distance covered bythe particle in first 4 seconds is

For  𝑡≥ 0 , the velocity of a particle moving along the x-axis is given by  𝑣(𝑡) =𝑡3− 6𝑡2+ 10𝑡− 4 . At what time t does the direction of motion of the particle change from right to left?Responses0.5860.5861.1841.1842.0002.0002.816

At time 𝑡≥ 0 , a particle moving in the xy-plane has velocity vector given by 𝑣(𝑡)=〈3,2−𝑡2〉 . If the particle is at the point  (1,12) at time  𝑡= 0 , how far is the particle from the origin at time  𝑡= 1 ?Responses2.3042.3043.1073.1074.2094.2095.310

The x and y coordinates of the particle at any time t are x=at−bt2 and y=ct respectively, (where a,b and c are positive constant). The magnitude of acceleration of the particle at t=2 s is