Suppose the net force on an object with a mass of 2 kg is given by the following

Question

Suppose the net force on an object with a mass of 2 kg is given by the following mathematical formula: F(t)=(12t^2)i+(6e^-t)j where F is measured in Newtons and t is measured in seconds as usual. Assuming the object begins at rest, located at the origin, detetermine the object's:

a) acceleration

b)velocity

c)position vectors as fuctions of time t

Hint: If you don't know how to intergrate yet, you will have to figure this out by doing "antiderivatives": once you have a, guess a function v whose derivative is a.

Explanation / Answer

F = 12 t2 i + 6e-tj

a) Acceleration, a = F /m = (12 t2 i + 6e-tj ) / 2 = (6 t2 i + 3e-t j)

b) Velocity = Integral of acceleration; v = Int {(6 t2 i + 3e-tj) dt} = (2t3 i - 3e-t j)

c) position vector = Integral of velocity ; r = Int {(2t3 i - 3e-t j) dt} = (t4/2 i + 3e-t j)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.