Maths M1
Does anyone know how to find the equation for the distance travelled by the van in part (v) to enable me to get a quadratic equation and solve? Thank you!
This is what I did:
On the graph, I marked some unknown point 'T' in between 10 seconds and 24 seconds.
I already know the distances they had travelled up to 10 seconds, the van had done 170m, and the cyclist had covered 105m. But, because it was 93m ahead of the van, you add that on, making it 197m.
You are told that they overtake, so the distance travelled must be the same. Set up two equations, one for the van and one for the cyclist, and set them equal to each other.
Cyclist: 197 + 15(t-10)
Van: 170 + 17(t-10)
I got these equations by using the area under the curve, knowing that it is equivalent to the distance.
Set them equal to each other, and you get:
197 + 15(t-10) = 170 + 17(t-10)
Solve for 't':
2t = 47
Making t = 23.5 seconds.
That must mean the van only just overtook the cyclist for half a second before the cyclist went past him again.
Posted from TSR Mobile
On the graph, I marked some unknown point 'T' in between 10 seconds and 24 seconds.
I already know the distances they had travelled up to 10 seconds, the van had done 170m, and the cyclist had covered 105m. But, because it was 93m ahead of the van, you add that on, making it 197m.
You are told that they overtake, so the distance travelled must be the same. Set up two equations, one for the van and one for the cyclist, and set them equal to each other.
Cyclist: 197 + 15(t-10)
Van: 170 + 17(t-10)
I got these equations by using the area under the curve, knowing that it is equivalent to the distance.
Set them equal to each other, and you get:
197 + 15(t-10) = 170 + 17(t-10)
Solve for 't':
2t = 47
Making t = 23.5 seconds.
That must mean the van only just overtook the cyclist for half a second before the cyclist went past him again.
Posted from TSR Mobile
Original post by KatsuoK
What is the answer? Because that means I don't know either!
Well, that just proves how good I am at mechanics...
Well, that just proves how good I am at mechanics...
T=24 or T=198/17 =11.6
Therefore T=11.6.
I'm not sure about this question either if you can work out how to get it let me know thanks
!!Original post by j582
Help anyone!!
o.k. here goes
Equating positions after 24 secs we find that V=34 m.s^-1
Now for the last part.
deceleration of van is
Unparseable latex formula:
\frac{34}{14}\mathhrm{\ ms\ }^{-1}
So at time T, velocity of van is
Distance traveled by van is thus
Distance traveled by cyclist is
So again, equating their positions we eventually have the quadratic equation which has roots 11.65 and 24.
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