Question

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position.

a(t) = 7i + 4j, v(0) = k, r(0) = i
v(t) = ?
r(t) = ?

Answer 1

To find the velocity and position vectors, we can integrate the given acceleration function. The velocity function is v(t) = 7t i + 4t j + k, and the position function is r(t) = (3.5t^2 + kt)i + (2t^2)j + ki.

Step-by-step explanation:

To find the velocity and position vectors of a particle with the given acceleration, initial velocity, and position, we can integrate the acceleration function to obtain the velocity function and integrate the velocity function to obtain the position function.

velocity function: v(t) = integral(a(t) dt) = 7t i + 4t j + k

position function: r(t) = integral(v(t) dt) = (3.5t^2 + kt)i + (2t^2)j + ki

Therefore, the velocity vector at any time t is v(t) = 7t i + 4t j + k, and the position vector at any time t is r(t) = (3.5t^2 + kt)i + (2t^2)j + ki