Question

A 18.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by

= 7t²î + 3tĵ

where  is in meters per second and t is in seconds. (Use the following as necessary: t.)

(a) Find its position as a function of time.
=

b) Describe its motion qualitatively.

This answer has not been graded yet.

(c) Find its acceleration as a function of time.
=

m/s²

(d) Find the net force exerted on the particle as a function of time.
=

N

(e) Find the net torque about the origin exerted on the particle as a function of time.
τ =

N · m

(f) Find the angular momentum of the particle as a function of time.
=

kg · m²/s

(g) Find the kinetic energy of the particle as a function of time.
K =

J

(h) Find the power injected into the particle as a function of time.
P =

W

Answer 1

given

m = 18 kg

v = 7 t² î + 3 t ĵ

a )

x = $\int$ v.dt

= $\int$ ( 7 t² î + 3 t ĵ ) . dt

= 7 ( t³ / 3 ) i + 3 ( t² / 2 ) j

x = ( 2.33 t³ i + 1.5 t² j ) m

b )

to describe its motion that

if the vectors x and v parallel to each of them then the motion of the particle obviously in straight line,

but this is based on the vectors.

c )

acceleration = rate of change of velocity with respect to time

a = dv / dt

= d ( 7 t² î + 3 t ĵ ) / dt

= 7 x 2 t i + 3 j

a = ( 14 t i + 3 j ) m/sec²  

d )

the net force exerted on the particle as a function of time " F "

F = m a

= 18 x ( 14 t i + 3 j )

F = ( 252 t i + 54 j ) N