How many seconds after the driver applies the brakes does the car come to a stop?

The driver of a car traveling at 36 ft/s suddenly applies the breaks. The position of the car is s = 36t - 3t^2, t seconds after the driver applies the breaks. How many seconds after the driver applies the brakes does the car come to a stop?



A. 6 sec

B. 18 sec

C. 36 sec

D. 12 secHow many seconds after the driver applies the brakes does the car come to a stop?I am going with B, as it is the most logical of the answersHow many seconds after the driver applies the brakes does the car come to a stop?BHow many seconds after the driver applies the brakes does the car come to a stop?s=36t-3t^2



ds/dt=36-6t



ds/dt=0 when the cars is stopped



0=36-6t

36=6t

t=6

the car takes 6 seconds to stopHow many seconds after the driver applies the brakes does the car come to a stop?v = ds/dt = 36 - 6t

v = 0 at

36-6t = 0

t = 6



Ans: A

_____________.How many seconds after the driver applies the brakes does the car come to a stop?the speed is ds/dt = 36 - 6t

it comes to stop when speed is zero or 36-6t = 0

t = 6

so AHow many seconds after the driver applies the brakes does the car come to a stop?s = 36t - 3t^2



velocity, v, = d/dt of s = d/dt of 36t - 3t^2 = 36 - 3(2t) = 36 - 6t



For the car to come to a stop, velocity, v, must be 0.

thus, 36 - 6t = 0 =%26gt; 6t = 36 =%26gt; t = 36/6 = 6 seconds.



Thus, the car comes to a stop 6 seconds after applying the brakes.

Thus, correct answer is A.How many seconds after the driver applies the brakes does the car come to a stop?6 sec

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