Acar is traveling at a constant velocity of magnitude v0 when the driver notices a garbage can on the road in front of him. at that moment, the distance between the garbage can and the front of the car is
d. a time t after noticing the garbage can, the driver applies the brakes and slows down at a constant rate before coming to a halt just before the garbage can. what is the magnitude of the car's acceleration after the brakes are applied?

The magnitude of the acceleration of the car is

The given parameters;

To find:

The distance traveled by the  car  before the driver discovers the garbage;

The new distance between the driver and garbage;

The magnitude of the acceleration of the car is calculated as;

when the driver reaches the final distance () after the breaks are  applied, the final velocity () of the car will be zero.

Thus, the magnitude of the acceleration of the car is

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Explanation:

distance moved by the car while the driver reacted to apply brakes is given as

now the distance of the car from the position of garbage is given as

now if driver applies rakes due to which car decelerates uniformly and comes to rest

so we have

increase masses, decrease separation

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