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?
This question was asked and answered elsewhere. The answer is 450 + 900 = 1350 km, It takes twice as far to declerate as it does to accelerate, because the deceleration rate is half of the acceleration rate.
To find the distance the dragster has traveled before stopping, we can divide the problem into two parts: the initial acceleration phase and the deceleration phase.
For the initial acceleration phase:
We can use the kinematic equation: distance = (initial velocity × time) + (0.5 × acceleration × time^2) to find the distance traveled during this phase.
Given:
Initial velocity (u) = 0 m/s (as the dragster starts from rest)
Acceleration (a) = 14 m/s^2
Distance (s) = 450 m
Using the equation, we have:
450 = 0.5 × 14 × t^2
Divide both sides by 0.5 × 14:
t^2 = (450 / 7)
t^2 = 64.29
Take the square root of both sides:
t = √(64.29)
t ≈ 8.02 seconds
So, during the initial acceleration phase, the dragster travels for approximately 8.02 seconds.
Now, for the deceleration phase:
We can use again a similar kinematic equation to find the distance, but this time, the acceleration will be negative as it is decelerating.
Given:
Initial velocity (u) = 14 m/s (which is the final velocity during the initial phase)
Acceleration (a) = -7 m/s^2 (negative because it's decelerating)
Final velocity (v) = 0 m/s (as the dragster comes to a stop)
Distance (s) =?
Using the same equation, but rearranging it to solve for distance, we have:
distance = (0.5 × (v + u) × t)
Plugging in the values, we get:
distance = (0.5 × (0 + 14) × 8.02)
distance ≈ 56.28 meters
During the deceleration phase, the dragster travels approximately 56.28 meters.
Therefore, the total distance traveled before stopping is the sum of the distances during both phases:
Total distance = distance of initial acceleration phase + distance of deceleration phase
Total distance = 450 meters + 56.28 meters
Total distance ≈ 506.28 meters