Two cameras are placed 90 m apart along a highway, with each camera taking a pic

Question

Two cameras are placed 90 m apart along a highway, with each camera taking a picture the moment a car passes the camera. The speed limit on the highway is 100 km/h. A car approaches the first camera. The motorist starts braking with constant acceleration of magnitude 3.5 m/s 2 as he passes the first camera and then maintains this constant acceleration until he has passed the second camera. The time stamps show that the time difference between the two photographs is 3.2 s. Given this information, find out whether the car had been speeding at the first camera, and how fast it is going when passing the second camera. In writing out your solution, follow the steps below.

List all the known and unknown variables. Make sure you include the signs of known quantities. For quantities that require calculation, assign them variables (do not assign any numerical values). Check how many unknowns there are in the problem. (c) Identify the equation(s) of motion to use. If possible, choose one equation of motion that has only one unknown of interest. Otherwise, identify two equations in two unknowns. You need the same number of (independent) equations and unknowns. (d) Solve for the unknown quantity in the equation(s) you identified. Then solve for the other unknowns as appropriate. (e) Check that your answers make sense. This is a really good thing to do whenever you’re done with a problem—not only does it help you spot errors, but it also enhances your understanding of the physics involved.

Explanation / Answer

speed at first camera=100 km/hr=27.78 m/s

deaccleration=3.5 m/s^2

time=3.2 s

using newton equation

v=u+at

we get

v=speed at second camera=16.58 m/s=59.68 km/hr

Car has been speeding down between first and second camera

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