a driver of a car traveling at 17.3 m/s applies the brakes causing a uniform deceleration of 2.8m/s^2. How long does it take the car to accelerate to a final speed of 13.5 m/s?
V = Vo + a*t.
V = 13.5 m/s.
Vo = 17.3 m/s.
a = -2.8 m/s^2.
t = ?.
To find the time it takes for the car to decelerate from 17.3 m/s to 13.5 m/s, we can use the following formula:
Final velocity (vf) = Initial velocity (vi) + (acceleration * time)
Given:
Initial velocity (vi) = 17.3 m/s
Final velocity (vf) = 13.5 m/s
Acceleration (a) = -2.8 m/s^2 (negative because it's deceleration)
We need to rearrange the formula to solve for time (t):
vf = vi + (a * t)
Substituting the known values:
13.5 m/s = 17.3 m/s + (-2.8 m/s^2) * t
Now, we can solve for time:
13.5 m/s - 17.3 m/s = -2.8 m/s^2 * t
-3.8 m/s = -2.8 m/s^2 * t
Divide both sides by -2.8 m/s^2:
t = (-3.8 m/s) / (-2.8 m/s^2)
t ≈ 1.36 seconds
Therefore, it takes approximately 1.36 seconds for the car to decelerate from 17.3 m/s to 13.5 m/s.