Can you check if my answer is correct..?

Question

1)What is the average speed of an MRT train if it takes 30 minutes to travel 30 km from North Edsa to Pasay Taft station?
they said the answer is 60 km/h

2) A car starts from rest and is uniformly accelerated to a speed of 30 m/s in 6 s. What distance does the car travel?
they said the answer is 90 m

My answer in #1 is 1 km/h but they said its wrong and my answer in #2 is 5 m but they said its wrong..
please show me why did they say that the answer in #1 is 60 km/h and the answer in #2 is 90 m.

why?? how it became the answer is 60 km/h and 90 m????
a.s.a.p

Answer 1

Question #1)
Advice: If you want your answer to be in units of km per hour, then the units of distance and time you use to calculate the speed should also be in km and hours.
60 minutes = 1 hour,
30 minutes = 1/2 hour

Speed = distance / time
Speed = 30 km / 30 minutes = 30 km / .5 hours
Speed = 60 km/h


Question #2)
Advice: The formula you need to use is: d = 1/2 at^2
But to find a, you need to use: a = v / t.

The car's speed starts at 0 m/s and accelerates to 30 m/s, so the change in velocity is 30 m/s. This change in velocity occurs in 6 seconds, so the time is 6 s.
a = 30 m/s / 6 s
a = 5 m/s^2

Now to find the the distance...
we already know the time is 6 seconds. We also just found the acceleration, 5 m/s^2.
d = 1/2 at^2
d = 1/2 * (5 m/s^2) * (6 s)^2
d = 2.5 m/s^2 * 36 s^2
d = 90 meters


So both of the answers I calculated come out to be the same value as the questions say they should. Hope you understood the steps I took to get to the answer.

Answer 2

For number one: Average Speed = Total Distance Travelled / Total Time taken. Remember that 30 minutes is 0.5hours. That is 30km / 0.5 hrs. = 60km/hr.
For number 2: First we need to find the acceleration. Using v = u + a*t, where v is final velocity = 30m/s and u is initial velocity = 0, and a is acceleration = unknown, and t is time = 6seconds. Then 30 = 0 + a *6 then a = 5.

Now use s = u*t + 1/2 a*t^2. where s is distance which is unknown. Then we get s = 0 + 1/2 *5*6*6 = 90m.


Those are Newtons equations of motion. There are three of them. Learn then and use them always for questions like these.

Answer 3

1) The units you are using are in Hours not Minutes. So it took 1/2 hour to go 30 km. 30/(1/2) = 60 km/h

2) d = 1/2 at^2

to get acceleration, divide m/s by s = 5 m/s^2
so 1/2 5(6^2) = 90 m

Answer 4

Both their answers are correct as In 1st case time is 1/2 hrs(0.5 hrs).
Speed=Distance/time=30/0.5=60 km/hr
In second case the car is accelerated to 30m/s in 6 seconds. Initially it was at rest. This can be derived using kinematical equations also but roughly:-
Average SPeed= Initial speed+Final Speed/2=0+30/2=15m/s
As car travels distance 15 metres in 1 second, distance travlled in 6 seconds is 15*6=90m

Answer 5

1) If you convert the time frame of 30 minutes to an hour (so that you can guage the speed in Km/H) you will have 0.5 hours.

Speed = Distance/Time

Distance = 30km
Time = 0.5 hours

Therefore:

Speed = 30/0.5
Speed = 60km/h

2) Not sure about this (been along time since I did this!)