Motion qn help

[ttn]

Is there a quick and easy way to solve these types of problems? The way I did it was a bit too long and complicated.

A motorist is travelling at a constant speed of 120km/h along a freeway when he passes a stationary police car. The police car immediately gives chase, accelerating at 2.4m/s^2 to a speed of 48m/s.

Find the time taken for the police car to catch the motorist.

[xZero]

Draw a graph (v to t) for the motorist and the police car. Then equate the area below the graphs to find the time

[ttn]

I've got the graph drawn, but how do I go about equaling the area?

[xZero]

firstly, let t = time taken for the police car to catch up
so the area under the police car graph should be a trapezium and the motorist should be a square
the area of the motorist should be 120/3.6 x t(remember to convert it to m/s)
the area of the police car should be 0.5 x 48 x ( (t-20) + t)

rest should be simple

Edit: opps haha hate these small mistakes

[ttn]

I equaled them and it's not getting the right answer?

[ttn]

Oh nvm, typed it wrong in calc, but your police car formula is wrong, it should be  0.5 x 48 x ( (t-20) + t), plus not multiply.

Thanks for the help.