Question

A car of length 4.3m is traveling at 105km/h. It passes over a bridge of length 36m. Calculate the time, in seconds; it takes to pass over the bridge completely.

Answer 1

Hint: The term speed generally refers to the average speed of a journey and is defined as the ratio of distance covered to unit time.
Speed (S) = $\dfrac{{{\text{Distance (D)}}}}{{{\text{Time (T)}}}}$
Units Conversion: Conversion of units is important here
$\begin{gathered}
  1\dfrac{{km}}{h} = \dfrac{{1km}}{h} \times \dfrac{{1000m}}{{1km}} \times \dfrac{{1hr}}{{3600s}} = \dfrac{{1000m}}{{3600s}} = \dfrac{5}{{18}}\dfrac{m}{s} \\
  1\dfrac{m}{s} = \dfrac{{1m}}{s} \times \dfrac{{1km}}{{1000m}} \times \dfrac{{3600s}}{{1hr}} = \dfrac{{3600km}}{{1000hr}} = \dfrac{{18}}{5}\dfrac{{km}}{h} \\
\end{gathered} $
When a car of length L passes a bridge of length D, the distance travelled by the car to cross the bridge is the sum of the lengths of the bridge and the car (L+D).

Complete step-by-step answer:
It is given that –
Length of the car = 4.3m
Car is moving with speed = 105km/h
We need to calculate the speed in m/s as other terms are in meter, so firstly we have to convert the units.
So, to convert the speed in m/s we have to multiply it by $\dfrac{5}{{18}}$
$\therefore 105km/h = 105 \times \dfrac{5}{{18}} = 29.167m/s$
Therefore, the speed of the car = 29.167m/s
For the car to completely pass the bridge, back end of car should cross the endpoint of bridge.
Distance covered by the car to cross the bridge = (Length of the car + Length of the bridge)
$\begin{gathered}
   = \left( {4.3 + 36} \right) \\
   = 40.3 \\
\end{gathered} $
Now to calculate the time taken to cross the bridge completely is equal to,
Time taken = Total distance/Speed of the car
Time taken = $\dfrac{{40.3}}{{29.167}}$
Time taken = $1.381$
So, car takes 1.381 seconds to pass over the bridge completely.
Note: In the case of the car passing a pole or other objects of negligible length, the distance traveled will be equal to the length of the car. In these types of problems, where the object is long and its length also needs to be considered while computing the distance.