How much time does it take for a car to come to rest if it has an initial speed of 22m/s and slows with a deceleration of 6.1 m/s^2
Will my answer be 3.6 m/s^2
Units of time are seconds, minutes, and
hours.
Vf = Vo + a*t = 0.
t = -Vo/a = -22/-6.1 = 3.61 s.
Well, that's not a clown-worthy mistake, but close enough! The deceleration you provided is -6.1 m/s^2, which means it's a negative value indicating slowing down. So, your answer will be the time it takes for the car to come to rest.
To find the time it takes for a car to come to rest, given its initial speed and deceleration, we can use the following formula:
v = u + at
Where:
v = final velocity (0 m/s, since the car comes to rest)
u = initial velocity (22 m/s)
a = acceleration (deceleration in this case, which is -6.1 m/s^2)
t = time
Rearranging the formula to solve for t:
t = (v - u) / a
Substituting the given values:
t = (0 - 22) / -6.1
Simplifying:
t = -22 / -6.1
t ≈ 3.61 seconds
Therefore, it takes approximately 3.61 seconds for the car to come to rest.
No, your answer will not be 3.6 m/s^2. The value of 3.6 m/s^2 is the acceleration due to gravity, not the deceleration of the car.
To determine the time it takes for the car to come to a rest, you can use the equation:
v^2 = u^2 + 2as
Where:
- v is the final velocity (which is 0, since the car comes to rest)
- u is the initial velocity (given as 22 m/s)
- a is the deceleration (given as 6.1 m/s^2)
- s is the distance traveled
Rearranging the equation to solve for s (distance traveled):
s = (v^2 - u^2) / (2a)
Plugging in the given values:
s = (0^2 - 22^2) / (2 * -6.1)
Simplifying the equation:
s = (-484) / (-12.2)
s = 39.67 meters
Now that we know the distance traveled, we can use the kinematic equation:
v = u + at
Where:
- v is the final velocity (which is 0, since the car comes to rest)
- u is the initial velocity (given as 22 m/s)
- a is the deceleration (given as -6.1 m/s^2)
- t is the time
Rearranging the equation:
0 = 22 + (-6.1)t
-6.1t = -22
t = 22 / 6.1
t ≈ 3.61 seconds
Therefore, it will take approximately 3.61 seconds (rounded to two decimal places) for the car to come to a rest.