Edexcel AS Mechanics 1 revise doubt

Hi, I worked out a question in the revision guide of edexcel AS mechanics and I got the answer 50 but in the answers it says that it is 42 not 50. I have no idea how that answer could be worked out. Please help me. This is the question:

A car is travelling along a straight motorway at a constant speed V m/s. Ten seconds after passing a speed-limit sign, the driver brakes and the car decelerates uniformly for 5 seconds, reducing its speed to 30m/s. Given that the car covers a distance of 600m in the 15 second period, find the value of V.

Anyone, suggestions please?

Reply 1

atomicjellyfish

so if you draw a velocity time graph, the area under the graph should be equal to 600 between 1 and 15 seconds.
The area under the graph = 10V + 5(V-30)/2 + 150 = 600
450=10V + 5/2V -75
525=12.5V
V=42