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A car travelling with a constant speed of 80km/hr passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80km/hr in 10 seconds and reaching a constant speed of 100km/hr after a further 5 seconds. At what time will the policeman catch up with the car?

The past questions I have been doing in the same section have been about graphs, I think that this is the same but I'm stumped. I then thought about putting two equations together and cancelling but this worked to no avail as way. The working for the equations is below but I wasn't sure about how to put the working for that here

Any help would be greatly appreciated

x=ut+1/2at^2

and

x=vt-1/2at^2

I put these two together and got

ut+1/2at^2=vt-1/2at^2

I rearranged to get

u2t/4at^4

That is where I got stuck because I wasn't sure how to rearrange

The past questions I have been doing in the same section have been about graphs, I think that this is the same but I'm stumped. I then thought about putting two equations together and cancelling but this worked to no avail as way. The working for the equations is below but I wasn't sure about how to put the working for that here

Any help would be greatly appreciated

x=ut+1/2at^2

and

x=vt-1/2at^2

I put these two together and got

ut+1/2at^2=vt-1/2at^2

I rearranged to get

u2t/4at^4

That is where I got stuck because I wasn't sure how to rearrange

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