A car’s position is given bys = 25t + t^2where s is in metres and t is in seconds. The car passesa police car that is travelling at 20 m/s. The police officer turns on the siren and begins to accelerateat 1.5 m/s^2 to chase the speeding car. The velocity of the police car is given byv =1.5t + 20

a) When is the speeding car travelling at 31 m/s?

b) How fast is the police car travelling at that time?

c) How far apart are the two cars at that time?

d) Will the police car ever catch up to the speeder?

For c), how would you find the displacement of the cop car?

and for d), is an inequality used?

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