The position of a particle for t > 0 is given by ⃗ =(m.

(a) what is the velocity as a function of time?
(b) what is the acceleration as a function of time?
(c) what is the particle’s velocity at t = 2.0 s?
(d) what is its speed at t = 1.0 s and t = 3.0 s?
(e) what is the average velocity between t = 1.0 s and t = 2.0 s?

(a)

(b)

(c)

(d) = 22.41 m/s; = 189.92 m/s

(e) average velocity = (9i-21j-5) m/s

Explanation:

For the given problem:

(a) The velocity as a function of time: v(t) = dr/dt. Thus:

(b) The acceleration as a function of time: a(t) = dv/dt. Thus:

(c) The particle velocity at t= 2.0s. Using the equation in part (a);

(d) Its speed at t=1.0s and t=3.0s

at t=1.0s

= 22.41 m/s

at t= 3.0s

= 189.92 m/s

(e)  The average velocity between t = 1.0 s and t = 2.0 s. Using the equation for r(t).

m

average velocity = Δr/Δt = (r2-r1)/(t2-t1) = (9i-21j-5) m/s

magnityde and direction