Suppose a cars brakes can produce an acceleration of -7m/s^2. If the car is traveling at an initial speed of 28m/s, what is the minimum distance necessary to stop the car?
d = (V^2-)Vo^2)/2a.
d = (0-(28)^2) / -14 = 56 M.
To find the minimum distance necessary to stop the car, we need to use the kinematic equation that relates initial velocity, acceleration, and distance.
The equation we can use in this case is:
v^2 = u^2 + 2as
where:
- v is the final velocity (which is 0 since the car needs to stop),
- u is the initial velocity (28 m/s),
- a is the acceleration (-7 m/s^2),
- s is the distance traveled.
Rearranging the equation to solve for s, we have:
s = (v^2 - u^2) / (2a)
Substituting the values, we get:
s = (0^2 - 28^2) / (2 * -7)
s = (-784) / (-14)
s = 56 meters
Therefore, the minimum distance necessary to stop the car is 56 meters.