Question

A particle initially located at the origin has an acceleration of vector a = 2.00ĵ m/s2 and an initial velocity of vector v i = 9.00î m/s.(a) find the vector position of the particle at any time t (where t is measured in seconds).

Answer 1

To find the vector position of the particle at any time t, use the kinematic equation r(t) = r0 + vit + 0.5at2. Plug in the values for the initial velocity and acceleration to get the position function.

Step-by-step explanation:

Given that at time t, the particle has an acceleration of vector a = 2.00ĵ m/s2 and an initial velocity of vector vi = 9.00î m/s, we can find the vector position of the particle at any time t using the kinematic equations.

The position function is given by:

r(t) = r0 + vit + 0.5at2

Plugging in the values, we have:

r(t) = 0 + (9.00î m/s)(t) + 0.5(2.00ĵ m/s2)(t2)

So, the vector position of the particle at any time t is r(t) = 9.00tî + t2ĵ - t2 km.

Answer 2

The position S(t) at any time of the particle can be written as

`S(t)=S_0 + vt + (1)/(2)at^2`
where
`S_0` is the initial position (in our case, the particle is initially located at the origin, so S0=0i+0j, v is the velocity, a the acceleration and t the time.

Using v(t)=9.00 i m/s and a(t)=2.00 j m/s^2, we can rewrite S(t), the vector position of the particle at time t:

`S(t)=9t \mbox{\bf{i}} m/s + (1)/(2) 2 t^2 \mbox{\bf{j}} m/s^2`