To determine the values of the constants "c" and "k" in the equation v = kt² - Ct, we'll need to use the given information about acceleration and time.
Given: Acceleration (a) = 6 m/s² Time (t) = 2 s
First, we can differentiate the equation v = kt² - Ct with respect to time (t) to find the expression for acceleration (a).
dv/dt = d(kt² - Ct)/dt
Using the power rule of differentiation, we get:
a = 2kt - C
Since the acceleration is given as 6 m/s² after 2 seconds, we can substitute these values into the equation:
6 = 2k(2) - C 6 = 4k - C
This is the first equation we obtain.
Now, let's consider the given equation v = kt² - Ct and find its derivative with respect to time (t) to get the expression for velocity (v).
dv/dt = d(kt² - Ct)/dt
Again, using the power rule of differentiation:
v = 2kt - C
Since we know the value of velocity after 2 seconds, we can substitute these values into the equation:
v = 2k(2) - C v = 4k - C
This is the second equation we obtain.
We now have two equations with two unknowns (k and C). We can solve this system of equations simultaneously. Substituting the value of v from the second equation into the first equation, we have:
6 = 4k - C
Substituting 4k - C = 6 into the first equation, we get:
6 = 6
This shows that 6 = 6, which is true. It means the equation v = kt² - Ct is consistent with the given information.
Since there are infinitely many solutions for k and C that satisfy the equations, we cannot determine unique values for these constants without additional information.