A car traveling at 43 ft/sec decelerates at a constant 5 feet per second squared. How many feet does the car travel before coming to a complete stop?
i tried a few different equations, none of the worked.
43t - 5t^2 = 0
43 - 10t = 0
21.5t^2 - (5/3)t^3 = 0
maybe im not supposed to set it to zero? i don't know what to do
This looks like the "anti-derivative" question I answered earlier this evening.
The equation you need to solve is:
d = 43t - 5t^2
To find the total distance traveled, you need to integrate this equation. The integral of d is:
D = 43t^2/2 - 5t^3/3
To find the total distance traveled before coming to a complete stop, you need to set t = 0 and t = the time it takes for the car to come to a complete stop. To find the time it takes for the car to come to a complete stop, you need to solve the equation:
43t - 5t^2 = 0
This equation can be solved using the quadratic formula:
t = (43 ± √(43^2 - 4(5)(0))/2(5)
t = (43 ± √1849)/10
t = 8.3 or t = 0
Since t = 0 is not a valid solution, the time it takes for the car to come to a complete stop is 8.3 seconds.
To find the total distance traveled before coming to a complete stop, plug t = 8.3 into the equation for D:
D = 43(8.3)^2/2 - 5(8.3)^3/3
D = 1745.7 feet
To find the distance traveled by the car before coming to a complete stop, you can use the equation of motion for uniformly decelerating motion. The equation is:
v^2 = u^2 - 2as
Where:
v = final velocity (which is 0 because the car comes to a complete stop)
u = initial velocity (given as 43 ft/sec)
a = acceleration (given as -5 ft/sec^2, negative because it's decelerating)
s = distance traveled
We can rearrange the equation to solve for s:
s = (u^2 - v^2) / (2a)
Plugging in the given values, we get:
s = (43^2 - 0^2) / (2 * -5)
Now, let's solve this equation step by step:
1. Calculate the numerator: 43^2 - 0^2 = 1849
2. Calculate the denominator: 2 * -5 = -10
3. Divide the numerator by the denominator: 1849 / -10 = -184.9
Since distance cannot be negative, it means we made a mistake in choosing the signs of the terms. Since we are looking for a positive distance, we need to take the absolute value of the result.
4. Calculate the absolute value of -184.9: 184.9
Therefore, the car travels approximately 184.9 feet before coming to a complete stop.
To find the distance the car will travel before coming to a complete stop, we can use the equation of motion:
d = (v^2 - u^2) / (2a)
Where:
- d is the distance traveled
- v is the final velocity (in this case, 0 ft/sec since the car comes to a complete stop)
- u is the initial velocity (43 ft/sec)
- a is the acceleration (deceleration in this case, -5 ft/sec^2)
Substituting the values into the equation, we have:
0 = (43^2 - u^2) / (2 * -5)
Simplifying further, we get:
0 = 1849 - u^2
u^2 = 1849
Taking the square root of both sides, we have:
u ≈ ± 43
Since we are given that the initial velocity is 43 ft/sec, we can ignore the negative value. So, u = 43 ft/sec.
Now we can substitute the values of u and a into the equation to find the distance traveled:
d = (0^2 - 43^2) / (2 * -5)
d = (-1849) / (-10)
d ≈ 184.9 ft
Therefore, the car will travel approximately 184.9 feet before coming to a complete stop.