A car comes to a stop in 6s from a velicity of 30m/s. what is its acceleration? At the same acceleration, how long would it take the car to come to a stop from a velocity of 40m/s?
v = Vi + a t
0 = 30 + a (6)
a = -5 m/s^2
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v = Vi - 5 t
0 = 40 - 5 t
t = 8 seconds
Well, well, well... look who decided to hit the brakes! To calculate the acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time
So, for the first scenario, we have:
acceleration = (0 m/s - 30 m/s) / 6 s
acceleration = -30 m/s / 6 s
acceleration = -5 m/s²
That negative sign indicates that the car is decelerating or slowing down. Now, let's find out how long it would take for the car to stop from a velocity of 40 m/s, assuming the same acceleration:
acceleration = (0 m/s - 40 m/s) / t
Now, let's solve for "t":
-5 m/s² = -40 m/s / t
Now, let's cross our fingers and do a little math:
5 m/s² * t = 40 m/s
t = 40 m/s / 5 m/s²
t = 8 s
So, using the same acceleration, it would take the car 8 seconds to come to a stop from a velocity of 40 m/s. Hang on tight and enjoy the ride!
To find the acceleration, we can use the formula:
acceleration = change in velocity / time
Given that the initial velocity is 30 m/s and it comes to a stop in 6 seconds, the change in velocity is (-30 m/s) - (0 m/s) = -30 m/s. (Note that the change in velocity is negative because the car is slowing down.)
Therefore, the acceleration is:
acceleration = (-30 m/s) / (6 s) = -5 m/s^2
Now, to find out how long it would take the car to come to a stop from a velocity of 40 m/s at the same acceleration, we can use the same formula.
Given that the initial velocity is 40 m/s and we want to find the time, the change in velocity is (-40 m/s) - (0 m/s) = -40 m/s.
Using the formula:
acceleration = change in velocity / time
Substituting the known values:
-5 m/s^2 = (-40 m/s) / time
To solve for time, we can rearrange the equation:
time = (-40 m/s) / (-5 m/s^2)
Simplifying:
time = 8 s
Therefore, it would take the car 8 seconds to come to a stop from a velocity of 40 m/s at the same acceleration.
To find the acceleration of the car, we can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 30 m/s
Final velocity (v) = 0 (since the car comes to a stop)
Time (t) = 6 s
Substituting the values into the formula:
acceleration = (0 - 30) / 6 = -5 m/s²
Therefore, the acceleration of the car is -5 m/s².
Now, to find how long it would take the car to come to a stop from a velocity of 40 m/s, we can rearrange the formula to solve for time:
time = (final velocity - initial velocity) / acceleration
Given:
Initial velocity (u) = 40 m/s
Final velocity (v) = 0 (since the car comes to a stop)
Acceleration (a) = -5 m/s²
Substituting the values into the formula:
time = (0 - 40) / (-5) = 8 s
Therefore, with the same acceleration, it would take the car 8 seconds to come to a stop from a velocity of 40 m/s.