Question

In: Advanced Math

(2) PQRS is a quadrilateral and M is the midpoint of PS. PQ = a, QR...

(2) PQRS is a quadrilateral and M is the midpoint of PS.
PQ = a, QR = b and SQ = a – 2b.
(a) Show that PS = 2b.
Answer(a)
[1]
(b) Write down the mathematical name for the quadrilateral PQRM, giving reasons for your answer.
Answer(b) .............................................................. because ...............................................................
............................................................................................................................................................. [2]
__________

A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations

Expert Solution

1.

a)

Let

By triangle law of vectors,

b)

Also,

since, and

Hence, PQRM must be a isosceles trapezium.

2)

Let the distance covered in the first 2 minutes be x1,

acceleration of the tram will be,

in the next 1 minute it continues to move uniformly with v=12m/s, hence

In the next 3 minutes, it decelerates to rest so deceleration would be,

Therefore, the total distance travelled will be,

Colby Messinger answered 2 years ago

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