Question
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?
Answers
GPT 3.5
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.
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.