Question

2. A particle has a constant acceleration of ?⃗ = (6.0 m s
2 ⁄ )?̂ + (4.0 m s
2 ⁄ )?. At ̂ ? = 0, the
velocity is zero and the position vector is ?⃗ 0 = (10 m)?̂.
(a) Find the velocity and position vectors as a function of time ?.
b)Find the equation of the particle’s path in the xy plane and sketch the path.

Answer 1

Given:

The acceleration of the particle is,

The velocity at time t=0 is,

The position vector of the particle at time t=0 is,

Part (a)

The velocity vector as a function of time is given by,

The position vector of the particle as a function of time is given by,

Part (b)

For the position vector of the particle, we can say that,

Eliminating the t from both equations, we get,

The path on xy plane will be: