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

Solutions

Expert Solution

Let

By triangle law of vectors,

Also,

since, and

Hence, PQRM must be a isosceles trapezium.

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 1 year ago

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