Question

Find the position and velocity of an object moving along a straight line with given acceleration, initial velocity, and initial position.

a(t) = -38, v(0) = 50, and s(0) = 10

Answer 1

To find the position and velocity of the object, we can integrate the acceleration function to find the velocity function, and then integrate the velocity function to find the position function.

The final velocity and position functions are v(t) = (10 − 2t)Î + 5ĵ + 5k m/s and s(t) = 10t - t^2 + 5t + 10 m, respectively.

Step-by-step explanation:

In order to find the position and velocity of an object moving along a straight line with given acceleration, initial velocity, and initial position, we can use the equations of motion. First, we can find the velocity as a function of time by integrating the acceleration function.

In this case, the velocity as a function of time is given by v(t) = (10 − 2t)Î + 5ĵ + 5k m/s. Next, we can find the position as a function of time by integrating the velocity function.

However, since the initial position is given as s(0) = 10, we need to take that into account when integrating. The position as a function of time is given by s(t) = 10t - t^2 + 5t + 10 m.