SOLUTION: 2. 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
Algebra.Com
Question 942123: 2. 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 a(t), velocity v(t), and position x(t), given that its initial acceleration, velocity, and position are a0, v0, and x0, respectively.
(b) Show that
NOTE: Finding the equations for motion with constant jerk is very similar to finding the equations for constant acceleration. Jerk is the derivative of acceleration ( J = da/dt ), and you already know that v = dx/dt and a = dv/dt. Just integrate in part (a) and rearrange in part (b) like we did in class when we derived the expressions for constant acceleration.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
a)
 = a_0 + \int_{0}^{t} J \, dt' = a_0 + Jt)
 = v_0 + \int_{0}^{t} a(t) \, dt' = v_0 + a_0t + \frac{1}{2}Jt^2)
 = x_0 + \int_0^{t} v(t) \, dt' = x_0 + v_0t + \frac{1}{2}a_0t^2 + \frac{1}{6}Jt^3)
b) You should specify what a_2 is. Not clear to us.
RELATED QUESTIONS
2. Suppose an object moves along the y-axis so that its location is y = f(x) = x^2 + x at (answered by ikleyn)
How does the amount of time an object moves affect how far it... (answered by Alan3354)
John drops an object from the top of a building that is 195 ft tall and calculates the... (answered by ewatrrr)
The velocity of an object as a function of time is V(x)= 8t-5. Calculate the acceleration (answered by ikleyn)
When a constant force is applied to an object, the acceleration of the object varies... (answered by josgarithmetic)
When a constant force is applied to an object, the acceleration of the object varies... (answered by Alan3354)
1.Give your examples of scalars and vectors.
2. Solve the problem involving uniform... (answered by rothauserc)
What is the acceleration of a car that moves from rest to 60.0ft/s in... (answered by Edwin McCravy)
An automotive repair shop has determined that the average service time on an automobile... (answered by stanbon)