The function D (t) = 16t^2 to the second power – 140t gives the distance a car going a certain speed will skid in t seconds. Find the time it would take for the car to skid 170 feet.
The time to skid 160 feet is __________ seconds.
I remember I gave you the solution process for this.
To find the time it would take for a car to skid 170 feet, we need to set up an equation and solve for t.
The given function D(t) = 16t^2 - 140t represents the distance (D) a car will skid in t seconds.
So, we need to solve the equation 16t^2 - 140t = 170.
To solve this equation, we can follow these steps:
Step 1: Subtract 170 from both sides of the equation:
16t^2 - 140t - 170 = 0.
Step 2: Simplify the equation:
16t^2 - 140t - 170 = 0.
Step 3: Factor the quadratic equation to solve for t:
(4t - 17)(4t + 10) = 0.
Step 4: Use the Zero Product Property to solve for t:
Set each factor equal to zero:
4t - 17 = 0 or 4t + 10 = 0.
Step 5: Solve for t in each equation:
For 4t - 17 = 0:
4t = 17,
t = 17/4,
t = 4.25 seconds.
For 4t + 10 = 0:
4t = -10,
t = -10/4,
t = -2.5 seconds.
Since time cannot be negative in this context, we ignore the negative solution.
Therefore, the time it would take for the car to skid 170 feet is 4.25 seconds.
To find the time it would take for the car to skid 160 feet, you can follow the same steps with the equation 16t^2 - 140t = 160. Solving the equation will give you the required time.