Question

A particle starts from the origin with velocity 5i m/s abd t=0 and moves in the xy plane with a constant acceleration of 6j. Determine the position of th particle after 5s.

Answer 1

The position of the particle after 5 seconds can be found using the formula for motion with constant acceleration, leading to a final position of (25, 75) meters in the xy-plane.

Step-by-step explanation:

To determine the position of a particle after 5 seconds when it starts from the origin with a velocity of 5i m/s and a constant acceleration of 6j m/s2, we can use the equations of motion. The position vector r(t) of the particle can be determined by integrating the velocity vector, which is the sum of the initial velocity and the product of acceleration and time.

The initial velocity vector of the particle is given as vi = 5i m/s, and the acceleration vector is a = 6j m/s2. To find the position after 5 seconds, we'll apply the formula r(t) = r0 + vit + (1/2)at2, where t is the time and r0 is the initial position.

Since the particle starts from the origin, r0 = 0, and the position vector becomes r(t) = (5i)(5) + (1/2)(6j)(52). Simplifying this, we get r(5s) = (25i + 75j) meters. Therefore, at t = 5 s, the particle is at the position (25, 75) in the xy-plane.