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The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

Verified Answer :

nobillionaireNobley

s(t) = 60t - 1.5t^2
Speed of the car is given by ds/dt = 60 - 3t
At the point the car stopped, speed = 0
60 - 3t = 0
3t = 60
t = 60/3 = 20
Therefore, the car stopped 20 minutes after the brake was applied.

JeanaShupp

Answer:- After 20 seconds the driver applied the brakes to stop the car.


Explanation:-

Given:- The position of the car \(s(t)=60t-1.5t^2\)

∴Speed of the car \(=\frac{ds}{dt}=\frac{d(60t-1.5t^2)}{dt}=60-3t\)

When car stopped the speed of car=0

\(\Rightarrow60-3t=0\\\Rightarrow3t=60\\\Rightarrow\ t=20\)

Therefore, after 20 seconds the driver applied the brakes to stop the car.

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