A car slows down at -5.00 m/s? until it comes to a stop after traveling 15.0 m. How much time does it take to stop?
To find the time it takes to stop, we can use the formula of motion:
v^2 = u^2 + 2as
where:
v = final velocity (0 m/s since the car comes to a stop)
u = initial velocity (-5.00 m/s)
a = acceleration (unknown)
s = displacement (15.0 m)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the values, we get:
a = (0^2 - (-5.00)^2) / (2 * 15.0)
a = (-25.0) / 30.0
a = -0.833 m/s^2
The acceleration is -0.833 m/s^2.
Now, we can use the equation of motion to find the time taken:
v = u + at
Since the car comes to a stop, the final velocity (v) is 0 m/s. Rearranging the equation, we have:
t = (v - u) / a
Substituting the values, we get:
t = (0 - (-5.00)) / -0.833
t = 5.00 / 0.833
t ≈ 6.01 seconds
Therefore, it takes approximately 6.01 seconds for the car to stop.
To find the time it takes for the car to stop, we can use the equation:
v² = u² + 2as
Where:
v is the final velocity (0 m/s in this case, as the car comes to a stop)
u is the initial velocity (-5.00 m/s)
a is the acceleration (unknown)
s is the distance traveled (15.0 m)
Rearranging the equation, we have:
a = (v² - u²) / (2s)
Substituting the values we know:
a = (0² - (-5.00 m/s)²) / (2 * 15.0 m)
Calculating the equation further:
a = (-25.00 m²/s²) / 30.0 m
a = -0.833 m/s² (rounded to three decimal places)
Now, we can use the equation for acceleration:
a = (v - u) / t
Substituting the known values:
-0.833 m/s² = (0 m/s - (-5.00 m/s)) / t
Simplifying the equation:
-0.833 m/s² = 5.00 m/s / t
Rearranging the equation:
t = 5.00 m/s / (-0.833 m/s²)
Calculating the equation further:
t = -5.999 s (rounded to three decimal places)
Therefore, it takes approximately 6.000 seconds (rounded to three decimal places) for the car to come to a stop.
To find the time it takes for the car to stop, we need to use the formula:
v = u + at
where:
- v is the final velocity (which is 0 m/s since the car comes to a stop),
- u is the initial velocity (which is -5.00 m/s),
- a is the acceleration (we assume it is constant, since it is slowing down),
- and t is the time.
We rearrange the formula to solve for t:
t = (v - u) / a
In this case, v is 0 m/s, u is -5.00 m/s, and a is unknown. Since the car is slowing down, the acceleration will be negative.
To find the acceleration, we use the equation:
a = (v - u) / t
In this equation, we know v is 0 m/s, u is -5.00 m/s, and t is unknown. Now we rearrange the formula to solve for t:
t = (v - u) / a
Since we know the car comes to a stop after traveling 15.0 m, we can also use the equation:
v^2 = u^2 + 2as
where:
- v is the final velocity (0 m/s),
- u is the initial velocity (-5.00 m/s),
- a is the acceleration (unknown),
- and s is the displacement (15.0 m).
Rearranging this equation, we can solve for a:
a = (v^2 - u^2) / (2s)
Substituting the values, we have:
a = (0^2 - (-5.00)^2) / (2 * 15.0)
Now we can substitute this value of acceleration into the equation we derived earlier to find the time it takes to stop:
t = (0 - (-5.00)) / (a)
Simplifying the equation, we get:
t = 5.00 / (a)
Now we can substitute the calculated value of acceleration into this equation to find the time it takes for the car to stop.