Question

The position of a particle as a function of time is given by

r(t)=(-3.0m/s)ti +(6.0m)j+[ 7.0m-(4.0m/s^3)t^3]k

a. what is the particle's displacement between t1=0 and t2=2.0s?

b. determine the particle's instantaneous velocity as a function of time.

c. what is the particle's average velocity between t1=0s and t2=2.0s?

d. Is there a time when the particle has a velocity of zero?

e. Determine the particle's instantaneous acceleration as a function of time?

Can you please explain the formulas you used and if any concepts as well for this problem.

Answer 1

we are given

r=xi^+yj^+zk^

here x and z are functions of t, y is independent of t

part a)

displacement of particle=|r|=(x²+y²+z²)^1/2

displacement of particle between this time=s1=(magnitude of r at 2 s-magnitude of r at 0 s)

part b)

instantaneous velocity=dr/dt

part c)

average velocity=s1/2

part d)

v=dr/dt

putting dr/dt=0

we can find t at which velocity is zero

part e)

a=d²r/dt²