- #1
fghtffyrdmns
- 145
- 0
Homework Statement
If s(0) = 0, v(1) = 24 and a(t) = 24t+6 find s(t)
Homework Equations
The Attempt at a Solution
I know a(t) is s''(t) and v(t) is s'(t). however, How can I find s(t)?
PAR said:Have you been given any equation relating s,v, and a?
SpicyPepper said:Find the anti-derivative of a(t), which is v(t).
Plug in t=1 for v(t) to get the constant.
The find the anti-derivative of v(t), which is s(t).
Plug in t=0 for s(t) to get the constant, and now you have your answer.
PAR said:almost, v(t) is incorrect, redo the derivative of s(t) to find the correct v(t)
fghtffyrdmns said:v(t) = 12t^2+6t
If I'm understanding your use of variables correctly, K is C.fghtffyrdmns said:See, this is what I don't understand.
would I just write 24 = 12t^2+6t +c?
the solve for c? where does the K come from?
yes, but C is not the same value or variable in both of those equations. C is just commonly used to represent an unknown constant.fghtffyrdmns said:v(t) = 12t^2+6t + C
s(t) = 4t^3+3t^2 + Kt +C
?
fghtffyrdmns said:I think I got it! My book doesn't even have this stuff in it. No, I was not skipping class. This teacher just gives us questions we've not even seen before. He does it all the time.
v(t) = 12t^2+6t
s(t) = 4t^3+3t^2 + t?
no?
not even close?
The constants in a motion equation refer to the fixed values that do not change throughout the motion, such as acceleration due to gravity or initial velocity. They are represented by letters or symbols in the equation and are used to calculate the motion of an object.
To find the constants in a motion equation, you will need to gather information about the motion, such as the initial velocity, acceleration, and displacement. Then, you can plug these values into the appropriate equations to solve for the constants.
Finding the constants in a motion equation allows us to accurately describe and predict the motion of an object. By knowing the values of these constants, we can calculate the position, velocity, and acceleration of an object at any given time during its motion.
No, the constants in a motion equation are fixed values and do not change throughout the motion. However, they may vary depending on different factors, such as the location or environment in which the motion is occurring.
The constants in a motion equation can be used in conjunction with other known variables to solve for unknown variables. For example, if we know the initial velocity and acceleration, we can use the equation v = u + at to solve for the final velocity. The constants provide a framework for solving for other variables in the motion equation.