A car slows to a stop with an average acceleration of - 3.0 m/s2. How long will it take to slow the car from 15 m/s to a position of rest?
To find the time it takes for the car to slow from 15 m/s to rest, we can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s in this case, as the car comes to rest)
u = initial velocity (15 m/s in this case)
a = acceleration (-3.0 m/s^2 in this case)
s = distance
Rearranging the equation, we have:
0^2 = 15^2 + 2(-3.0)s
Simplifying further:
0 = 225 - 6s
Rearranging the equation once more:
6s = 225
Dividing both sides by 6:
s = 37.5 m
So, the distance the car needs to travel to come to rest is 37.5 meters.
Now, we can use the equation for average acceleration to find the time:
a = (v - u) / t
Rearranging the equation, we have:
t = (v - u) / a
Substituting in the given values:
t = (0 - 15) / -3.0
Calculating further:
t = -15 / -3.0
t = 5 seconds
Therefore, it will take 5 seconds for the car to slow from 15 m/s to a position of rest.
To answer this question, we need to use the equation for acceleration:
acceleration = change in velocity / change in time
Given that the average acceleration is -3.0 m/s^2 and the initial velocity is 15 m/s, we can calculate the change in velocity by subtracting the final velocity (which is 0 m/s) from the initial velocity:
change in velocity = final velocity - initial velocity
change in velocity = 0 m/s - 15 m/s
change in velocity = -15 m/s
Now we can rearrange the equation to solve for change in time:
acceleration = change in velocity / change in time
Substituting the values we have:
-3.0 m/s^2 = -15 m/s / change in time
To isolate the change in time, we can multiply both sides of the equation by change in time:
-3.0 m/s^2 * change in time = -15 m/s
We can then solve for the change in time by dividing both sides of the equation by -3.0 m/s^2:
change in time = -15 m/s / -3.0 m/s^2
change in time = 5 seconds
Therefore, it will take 5 seconds to slow the car from 15 m/s to rest.