Question

Mechanics help?

Answer 1

i)Firstly you should sketch velocity time graph for this question with considering maximum velocity `v` and mentioning time on x-axis

As acceleration=gradient in velocity time graph
Or you can say
Acceleration=rise/run

Thus you can find velocity easily that will be `3=v/10`

So `v=20`m/s

And as they have asked you to find distance and in velocity time graph `distance=area under the graph`

Find area under the graph look at you rough sketch it will be the trapezim area

`1/2*`(length of parallel side)`*h`
height is the velocity you found above as `30`m/s

`1/2*(40+30)*30`

So you distance is `1050m`

ii)
(ii) Let the car comes to rest after seconds at B. (Assume)
And assume A is point (0,0) on graph

Total distance travelled by car=area of trapezium
`1500=1/2*(30)(30+t)`
`100=30+t`
`t=70`
The motor cycle starts 20s later
Thus,
total time taken by car from AtoB=`70-20`
That is `50`seconds

Total distance travelled by motorcycle=area of trapezim

That is `1500=1/2*V*(30+50)`

`1500=40V`
`v=37.5`m/s

maximum speed reached by motorcycle is, V 37.5 ms

motorcycle travels at constant speed for 30 seconds, therefore total time taken for acceleration and deceleration=20 seconds.

Let time taken for acceleration is t seconds, time taken for deceleration is (20-t)seconds given that., acceleration=3*deceleration

`(37.5/t)=3*((37.5)/(20-t))`

`20-t=3t`

`4t=20`

`t=5`s

Acceleration
a=`37.5/5`

`a=7.5`m/s^2

For iii) displacement time graph would be like this I am writing coordinates you can make it

`(0,0)`
`(10,150)`
`(40,1050)`
`(70,1500)`