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.)

Question

mani_jha · Answer

$$a(t)=ai+Jt$$
a(t)=dv(t)/dt.
$$dv(t)=aidt+Jtdt$$
Integrate from vi to v(t) to obtain expression for v(t).
Then write v(t)=dx/dt
dx=v(t)dt
Put this and integrate again from xi to x(t).