Question

Automotive engineers refer to the time rate of change of acceleration as the "jerk." Assume an object moves in one dimension such that its jerk J is constant.
(a) Determine expressions for its acceleration ax(t), velocity vx(t), and position x(t), given that its initial acceleration, velocity, and position are ai, vi, and xi, respectively. (Use any variable or symbol stated above as necessary.)

Answer 1

let j(t) be the jerk. Then by definition
\[ j(t) = \frac{d\ }{dt}a(t) \]
If j(t) is a constant, call it j, first find the solution to
\[ \frac{d\ }{dt} a(t) = j \]

Once you've done that, you keep on integrating to find v(t) and x(t)