A dragster accelerates from rest for a distance of 450m at 14 m/s^2. A parachute is then used to slow it down to a stop if the parachute gives the dragster an acceleration of -7m/s^2 how far has the dragster traveled before stopping?
To find the total distance traveled by the dragster before stopping, we can use the equations of motion for both the acceleration and deceleration phases.
First, let's calculate the distance covered during acceleration.
Given:
Initial velocity, u = 0 m/s (dragster starts from rest)
Acceleration, a = 14 m/s^2
Distance covered during acceleration, s1 = 450 m
We can use the equation of motion to find the time taken during acceleration:
v = u + at
Where:
v = final velocity (unknown)
u = initial velocity
a = acceleration
t = time
Since the dragster starts from rest, the initial velocity (u) is zero, so the equation becomes:
v = at
Substituting the values:
14 = a * t
Solving for t:
t = 14 / 14
t = 1 second
Now, we can use the equation of motion for distance to find the distance covered during acceleration:
s1 = ut + (1/2) a t^2
Substituting the values:
450 = 0 + (1/2) * 14 * (1)^2
450 = 7 * 1
450 = 7
Therefore, during the acceleration phase, the dragster covers a distance of 450 meters.
Next, we can calculate the distance covered during deceleration (using the parachute).
Given:
Acceleration during deceleration, a = -7 m/s^2
Final velocity, v = 0 m/s (the dragster comes to a stop)
Distance covered during deceleration, s2 = ?
Using the equation of motion for deceleration:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration (deceleration in this case)
s = distance
Substituting the values:
0^2 = v^2 + 2*(-7)*s2
0 = -14s2
Since the velocity (v) is zero, we can simplify the equation:
0 = -14s2
Therefore, during the deceleration phase, the dragster covers a distance of 0 meters (comes to a stop).
Now, to find the total distance traveled, we add the distances covered during acceleration and deceleration:
Total distance traveled = Distance during acceleration + Distance during deceleration
= 450 meters + 0 meters
= 450 meters
Therefore, the dragster has traveled a total distance of 450 meters before coming to a stop.
To find the distance traveled by the dragster before stopping, we need to calculate the distance covered during acceleration and during deceleration.
First, let's calculate the distance covered during acceleration.
We know the initial velocity (u) is 0 m/s (since the dragster starts from rest), the final velocity (v) is 14 m/s, and the acceleration (a) is 14 m/s^2.
We can use the equation:
v^2 = u^2 + 2as
Plugging in the values, we get:
(14 m/s)^2 = (0 m/s)^2 + 2 * 14 m/s^2 * s
Simplifying the equation:
196 m^2/s^2 = 28 m/s^2 * s
Dividing both sides of the equation by 28 m/s^2, we get:
s = 196 m^2/s^2 / 28 m/s^2
Simplifying further, we find:
s = 7 m
Therefore, the dragster travels 7 meters during acceleration.
Next, let's calculate the distance covered during deceleration.
We know the final velocity is 0 m/s (since the dragster comes to a stop) and the acceleration is -7 m/s^2.
Again, we can use the equation:
v^2 = u^2 + 2as
Plugging in the values, we get:
(0 m/s)^2 = v^2 + 2 * (-7 m/s^2) * s
Simplifying the equation:
0 m^2/s^2 = -14 m/s^2 * s
Dividing both sides of the equation by -14 m/s^2, we get:
s = 0 m^2/s^2 / -14 m/s^2
Simplifying further, we find:
s = 0
Therefore, the dragster travels 0 meters during deceleration since it comes to a stop.
Finally, to find the total distance traveled by the dragster, we sum the distances covered during acceleration and deceleration:
Total distance = Distance during acceleration + Distance during deceleration
Total distance = 7 meters + 0 meters
Total distance = 7 meters
Therefore, the dragster travels a total of 7 meters before coming to a stop.