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?

a.60 sec
b.40 sec
c.20 sec
d.10 sec

Question

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?

 a.60 sec
 b.40 sec
 c.20 sec
 d.10 sec

anonymous · Answer

do they give you the distance the car traveled in whatever time t?

noelgreco · Answer

Remember:
$$v=\frac{ ds }{ dt }$$

Differentiate, set v to zero.

anonymous · Answer

wait nvm, they gave u the position

anonymous · Answer

Okay, so what do I get as the answer?

anonymous · Answer

what is the derivative of s(t)?

anonymous · Answer

answer is C

anonymous · Answer

okAy can you please show me the steps on how you found that answer

anonymous · Answer

how far are you in math?

anonymous · Answer

my explanation will depend on that

anonymous · Answer

calculus

anonymous · Answer

have you taken the first physics yet?

anonymous · Answer

yes

anonymous · Answer

k so since the derivative of position gives you velocity, you can think of it as when the car will not be moving(velocity=0)

anonymous · Answer

when it hits the breaks, it will eventually come to a stop. what is the derivative of 60t-1.5t^2?

anonymous · Answer

when the car comes to a stop, you can measure how much time has passed by setting the velocity equation (derivative of s(t)) to zero, and solving for t.