Question

A particle of mass m is subjected to a force F along the x axis. Find its position as a function of time if it's starts moving from rest at t=0 and x=0

Answer 1

Answer:

F=−

x

2

k

m

dx

vdv

=−

x

2

k

vdv=−

m

k

x

2

dx

⇒∫

0

v

vdv=−

m

k

∫

a

x

x

2

dx

⇒

2

v

2

=[+

m

k

x

1

]

a

x

=

m

k

(

x

1

−

a

1

)⇒v=

m

2k

ax

(a−x)