Question

1) An 18-year-old runner can complete a 10.0 km course with an average speed of 4.52 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.07 m/s. How much later (in seconds) should the younger runner start in order to finish the the course at the same time as the older runner?
s

2) A sprinter explodes out of the starting block with an acceleration of +3.8 m/s², which she sustains for 1.4 s. Then, her acceleration drops to zero for the rest of the race.

(a) What is her velocity at t = 1.4 s.

m/s

(b) What is her velocity at the end of the race?

m/s

3) What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.4 m/s when going down a slope for 6.9 s?

m/s²

How far does the skier travel in this time?
m

Answer 1

1)

the delay in starting time of younger runner is the difference in time taken to complete the total distance
time taken by younger runner =(10km)/(4.07m/s)
= 2457 seconds
time taken by older runner =(10km)/(4.52m/s)
= 2212.389 seconds
so difference = 2457 seconds-2212.389 seconds
=244.61 seconds

2)

a)v=at so, answer 1 is 3.8 * 1.4 = 5.32 m/s.

b)After 1.4 seconds acceleration stops and she maintains a constant velocity, so 5.32 m/s is also the velocity at then end of the race.

3)

a) The average acceleration is A = V/T = 8.4/6.9 = 1.21739 m/s^2.

b) The average speed is Vavg = V/2 = 4.2 m/s. In T = 6.9 s, she will have traveled S = Vavg T = 4.

2*6.9 = 28.98 meters.

Answer 2

1) An 18-year-old runner can complete a 10.0 km course with an average speed of 4.52 m/s. A 50-year-old runner can cover the same distance with an average speed of 4.07 m/s. How much later (in seconds) should the younger runner start in order to finish the the course at the same time as the older runner?

18 year old runner distance 10 km - speed = 4.52 m/sec.
50 year old runner distance 10 km -4.07 m /sec
The distance is in km and speed in m/sec.
convert distance to meters
10km = 10,000 meters.

time taken by 18 year old = 10000/ 4.52
= 2212.38seconds
.==================================================
time taken by 50 year old = 10000/4.07
= 2457.00 seconds

2457.00 -

2212.38=

244.62=245

seconds

He can start

245

econds later to reach at the same time

Answer 3

1.       Time taken for 18 yr runner= 10000/4.52

=2212.39 sec

Time taken for 50 yr runner= 10000/4.07

=2457.00 sec

Delay which young runner should do=2457.00-2212.39

=244.61 sec=4 min 4.61 sec

2.       V= U+ at

V=0+ 1.4*3.8

=5.32 m/s

(b) As there is no further acceleration:

Velocity at end= 5.32 m/s

3.       V-U= at

8.4-0=a* 6.9

a= 1.217 m/s²

S= ut +

Answer 4

Answer 5

244.613,

5.32,

5.32,

1.21739,

57.96

Answer 6

1)time taken by 18 year old boy=10000/4.52=2212.389s

time taken by 50yr old runner=10000/4.07=2457.002s

difference time=244.613s

2)

a)velocity at 1.4 sec=3.8*1.4=5.32m/s

b) As there is no further acceleration:

Velocity at end= 5.32 m/s

3)v=u+at

8.4-0=a* 6.9

a= 1.217 m/s²

S= ut +

Answer 7

2) A sprinter explodes out of the starting block with an acceleration of +3.8 m/s², which she sustains for 1.4 s. Then, her acceleration drops to zero for the rest of the race.

(a) What is her velocity at t = 1.4 s.

V=Vo +a(t-to)= 0+(3.8 m/s² )1.4=5.32m/s---answer

(b) What is her velocity at the end of the race?

. Since her acceleration is zero during the remainder of the race, her velocity remains constant at

5.32m/s--answer

Answer 8

Answer 9

1)

10km=10,000m=x (distance)

v=4.52m/s

vt=x

x/v=t (divide both sides by v)

10,000m/(4.52m/s)=2212.39s=t

Older runner:

10,000m=x

4.07m/s=v

x/v=t

10,000m/(4.07m/s)=2457.00s

2457.00s-2212.39s=244.61s=4minute 4.61seconds

Since it takes the older runner 4 min 4.61 seconds longer to finish the course, the younger should wait that long before starting the course; then they'll both finish the course at the same time.

2)

3)a) By v = u + at

=>7.5 = 0 + a x 6.9

=>a = 1.08 m/s^2

(b) By s = ut + 1/2at^2

=>s = 0 + 1/2 x 1.08 x (6.9)^2

=>s = 102.8 m