The brakes of a car traveling at 16 m/s can decelerate it until it stops after 10m. Find (a) its negative acceleration, and (b) the time requires to stop

a. V^2 = Vo^2 + 2a*d

V = 0
Vo = 16 m/s
d = 10 m.
Solve for a.

b. V = Vo + a*t
V = 0
Vo = 16 m/s.
a = Value calculated in part a.
Solve for t.

99766

To find the negative acceleration, we can use the equation for acceleration:

acceleration = change in velocity / time

Given that the car starts with a velocity of 16 m/s and comes to a stop after a distance of 10 m, we can calculate the change in velocity as follows:

change in velocity = final velocity - initial velocity
change in velocity = 0 - 16
change in velocity = -16 m/s

The distance traveled can be expressed in terms of acceleration, initial velocity, and time as:

distance = (initial velocity * time) + (1/2 * acceleration * time^2)

Since we want to find the negative acceleration, we can rewrite the equation as:

10 = (16 * t) + (1/2 * a * t^2)

Simplifying the equation further, we get:

10 = 16t + (1/2 * a * t^2)

Since the car comes to a stop, the final velocity is 0, and we can set the equation equal to 0:

16t + (1/2 * a * t^2) = 0

To find the time required to stop, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1/2 * a, b = 16, and c = 0.

Plugging in the values, we get:

t = (-16 ± √(16^2 - 4 * (1/2 * a) * 0)) / (2 * (1/2 * a))
t = (-16 ± √256) / a
t = (-16 ± 16) / a

Solving for t, we get two possible solutions:

t1 = (16 - 16) / a = 0 / a = 0
t2 = (16 + 16) / a = 32 / a

Therefore, the time required to stop is either 0 seconds (immediate stop) or 32/a seconds (where a is the negative acceleration).

Hence, (a) the negative acceleration is -16 m/s^2, and (b) the time required to stop is either 0 seconds or 32/a seconds.

To find the negative acceleration of the car, we can use the formula:

Acceleration = Change in Velocity / Time

Given that the initial velocity (u) of the car is 16 m/s and the final velocity (v) is 0 m/s (since the car comes to a stop), we can substitute the values into the formula:

Acceleration = (v - u) / t

where v is the final velocity, u is the initial velocity, and t is the time.

Since v = 0 m/s, the formula becomes:

Acceleration = (0 - 16) / t

Simplifying this equation gives:

Acceleration = -16 / t

Therefore, the negative acceleration of the car is -16/t.

Now, let's determine the time required to stop the car.

We know that the car comes to a stop after traveling a distance of 10 meters. We can use the following equation to find the time:

Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2

Since the car comes to a stop, the final velocity is 0 m/s, and the equation becomes:

10 = 16 * t + 0.5 * (-16 / t) * t^2

Simplifying this equation gives:

10 = 16t - 8t

6t = 10

Dividing both sides by 6:

t = 10/6

t ≈ 1.67 seconds

Therefore, the time required to stop the car is approximately 1.67 seconds.