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.