The position of a particle that moves on a straight line is given by s(t) = t1/t for t > 0. A)Find the vel...

Question

The position of a particle that moves on a straight line is given by s(t) = t1/t for t > 0.

A)Find the velocity and acceleration

B) At what time, t, is the velocity zero? What is the acceleration at that time?

Answer 1

You differentiate position with respect to "t" to get velocity:

velocity=-t1/t^2 (t>0)


The velocity goes to zero as t goes to infinity.

acceleration = 2*t1/t^3. (i.e. differentiate velocity to get accel)

The acceleration at infinity is also zero.

Answer 2

A. v = -2t1/t^2
a=6t1/t^3

B. For v = 0, t approaches infinity for t1 != 0, at that time a = 0

Answer 3

A) Velocity is 1st derivative of position.
Acceleration is 2nd derivative of position (or 1st derivative of velocity).

B) See A, then use algebra.