Questions on linear motion?

Question

1) A car moves with uniform velocity, v1, for one-third of its journey. The car then moves with velocity v2=20 km/h to complete the journey. If the average velocity of the car is 27 km/h for the whole journey, find v1.

Can you pls show the formula and workings to complete this question? thank you!

2) A pupil runs round a circular field of radius 70 km. If he uses 40 minutes to complete one round, what is his velocity?
Is the answer 0km/min or 11km/min? Since velocity is related to displacement and the pupil's displacement remains 0.

Thank you for taking this time to answer my questions... =)

Answer 1

The average speed is
27=D/t3
and
20=2*D/(3*t2)
and
v1=D/(3*t1)
and
t1+t2=t3
solve for v1

20=2*D/(3*t2)
t2=D/30

27=D/t3
t3=D/27

t1+D/30=D/27
t1=D*(1/3*(1/9-1/10))

v1=1/(1/9-1/10)
v1=90

2) Is that 70 m or 70 km? I will assume 70 m. Since the total displacement is zero, the average velocity is zero. The average speed, on the other hand is

2*pi*70/(40)

11 m/min

j

Answer 2

let total dist. = x
x/3(v1) =x/3v1=total time taken for first half of the journey ...............(1)
for the second half the time taken =2/3of x/20=x/30 ..............(2)
total time= (1)+(2) ....................(3)
avg. velocity= x/(3)

we get on solving v1=90km per hr

2. radius(r)=70km
time taken=40 minutes

w.k.t velocityis related to diplacement which is a vector and it is simply a measure of the movement of the boy therefore since the pupil returns to the same place the diplacement remains zero
velocity=0kmperminute.

Answer 3

let dist =x

t1=x/3*v1
t2=2x/3*20


t1+t2=x/27

equatin above eqns

x/(3*v1)+2/60=x/27

1/(3*v1)+1/30=1/27

solve for v1