Question

The driver of a car traveling at 50 ft/sec suddenly applies the brakes. The position of the car is s(t) = 50t - 2t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

Answer 1

s(t) = 50t - 2t^2
v(t) = 50 - 4t
a(t) = -4

When v(t) = 0, the car stops.
v = u +at
0 = 50 + (-4)t
t=12.5s

Answer 2

Answer:

The car come to a stop in 12.5 seconds after the driver applies the brakes

Step-by-step explanation:

Given :The position of the car is $s(t) = 50t - 2t^ 2$, t seconds after the driver applies the brakes.

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

Solution:

$s(t) = 50t - 2t^ 2$

$V =\frac{ds}{dt}$

Where V is Speed of car

So, $V =\frac{d(50t - 2t^ 2)}{dt}$

$V =50-4t$

So,Speed of the car is  $V =50-4t$

Now we are supposed to find How many seconds after the driver applies the brakes does the car come to a stop.

So, Substitute V = 0

$0 =50-4t$

$4t=50$

$t=\frac{50}{4}$

$t=12.5$

Hence the car come to a stop in 12.5 seconds after the driver applies the brakes