Mechanics help?

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1 Answer
May 14, 2018

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=20m/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 30m/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 50seconds

Total distance travelled by motorcycle=area of trapezim

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

1500=40V
v=37.5m/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=5s

Acceleration
a=37.5/5

a=7.5m/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)