## Space Mountain Speed Profile

GCSE Text:
A roller coaster has a speed profile as shown in this graph below: a)  For how many seconds is the roller coaster travelling at a speed of at least 50km/hr?

b)  Estimate the maximum acceleration experienced during the ride

c)  Estimate the distance travelled during the entire ride (rounded to the nearest 100m)

Suggestions:
This is a complex but fun video showing some of the maths involved in ride design at theme parks. It requires to students to read and base calculations on velocity time graphs, therefore each student will ideally have a print out of the speed profile graph. Students take at least 5 minutes to complete this question, and many extension tasks can be used to stretch even more able students.

Extension Ideas:

Teachers could extend the learning by considering:

• Estimate the average speed throughout the ride (rounded to 1 d.p.)
• How could the estimate for distance be improved (which would also improve the estimate for average speed too)?
• Estimate the deceleration (or negative acceleration) which starts at 73 seconds