4MA0 Higher January 2018 Paper 3R Q13
13 A train travels at a constant speed of \(v\) kilometres per hour.
The train crosses a bridge.
The length of the bridge is \(b\) metres.
The length of the train is \(x\) metres.
\(T\) seconds is the time between the instant that the front of the train moves onto the bridge and the instant that the back of the train leaves the bridge.
Find a formula for \(T\) in terms of \(b\), \(x\) and \(v\).
Give your answer in its simplest form.
(3)
| Scheme | Marks |
|---|---|
| Total distance = \(b + x\) or \(v\) km/h = \(v \times 1000 \div 3600\) m/s | M1 |
| \((T =)\;(b + x)\,/\,(v \times 1000 \div 3600)\) | M1 |
| \(T = \dfrac{18(b + x)}{5v}\) | A1 |
| (3) |
Notes
M1: for total distance or conversion from km/h to m/s
M1: for any correct expression for \(T\)
A1: correct and fully simplified (numerator may not be factorised)