# Question #1ad1b

##### 1 Answer

#### Explanation:

Let use setup some variables to describe the problem:

# { (d, "total distance (or displacement) travelled"), (t_1, "time taken for first part of the journey"), (t_2, "time taken for second part of the journey"), (v_2, "velocity for second part of the journey") :} #

For the first part of the Journey:

# { (s, = 1/3d), (u, = v_1), (t, = t_1) :} # Applying

#s=ut# we have:

# 1/3d = v_1 t_1 # ..... [A]

For the second part of the Journey:

# { (s, = 2/3d), (u, = v_2), (t, = t_2) :} # Applying

#s=ut# we have:

# 2/3d = v_2 t_2 # ..... [B]

For the overall Journey:

# { (s, = d), (u, = 2v_1), (t, = t_1+t_2) :} # Applying

#s=ut# we have:

# d = 2v_1(t_1+ t_2 )# ..... [C]

From [A] and [C] we have:

# d = 3v_1 t_1 = 2v_1(t_1+ t_2 )#

# :. 3 t_1 = 2t_1+ 2t_2 #

# :. t_1 = 2t_2 #

So then from [C] we get:

# d = 2v_1(2t_2+ t_2 ) = 6v_1t_2#

Inserting into [B] we then have:

# 2/3 * 6v_1t_2 = v_2 t_2 #

# :. v_2 = 2/3 * 6v_1 = 4v_1#