Expert: Ahmed Salami - 11/27/2008

Question
A hovercraft, which has a max speed of 80km per hour, makes ajourney across the English Channel, a distance of 52km in 40mins. It is suggested that the velocity time graph has shape of an isoceles triangle. ( with peak at t=20mins,)

Comment on the likehood of this suggestion, with regard to velocity acceleration and time.

Answer
Hi Rg,
If the velocity-time graph has the shape of an isosceles triangle, this shows that there is constant linear acceleration for the first 20 mins and then an identical deceleration for the next 20 mins with a maximum velocity v(max) after the first 20 mins.
From the graph, the distance covered is the area of the triangle which is (20/60)hr x v(max) and this should be equal to 52km. Therefore,
v(max) = 156km/hr
This shows that there is a flaw in the suggestion.
Back to the hovercraft, 52km in 40mins means an average speed of
52/(40/60) = 78km/hr
At some point in the journey it would have a velocity greater than 78km/hr but not more than 80km/hr except it moves constantly at 78km/hr.

Regards.