brinstar said:Homework Statement
Calculate the position vector of a particle moving with velocity given by:
v = (32 m/s - (5 m/s^2 )t i) + (0 j)
Homework Equations
(x^(n+1) / (n+1) ) + C = antiderivative of function
The Attempt at a Solution
r = (32t m - (5/2)t^2 m/s + C m i) + (C j)
Honestly, I'm just confused with the units more than anything. I don't know why the problem has m/s^2 if it's a velocity vector...
SteamKing said:A quantity of 5 m/s2 indicates that accelerated motion is taking place, i.e., the velocity is changing w.r.t. time. Acceleration × time = change in velocity.
I would say that since the velocity vector had no j-component, the position vector will not either.brinstar said:oooooh okay that makes more sense. thank you!
and the antiderivative is right, right?
but isn't the antiderivative of 0 C (or in this case, D to differentiate)?SteamKing said:I would say that since the velocity vector had no j-component, the position vector will not either.
Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.brinstar said:but isn't the antiderivative of 0 C (or in this case, D to differentiate)?
SteamKing said:Yeah, but D = 0 would be an acceptable value for the constant of integration, in the absence of any other initial condition information.
You can have a definite integral only if you know the value of t.brinstar said:oh okay. since this is on a take home test, do you think I should just put both answers (one for a definite integral 0 and one for an indefinite integral D)?
SteamKing said:You can have a definite integral only if you know the value of t.
An antiderivative is the inverse operation of differentiation. It is a function that, when differentiated, gives back the original function.
Finding the antiderivative helps us to solve problems involving rates of change, such as motion and growth. It also allows us to find the area under a curve, which has many practical applications.
A vector is a quantity that has both magnitude and direction. It is commonly represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.
To find the antiderivative of a vector, you need to integrate each component of the vector separately. This can be done using the rules of integration, such as the power rule, product rule, and chain rule.
Sure, let's find the antiderivative of the vector (2x, 3x^2). The antiderivative of 2x is x^2 + C, where C is a constant. The antiderivative of 3x^2 is x^3 + C. Therefore, the antiderivative of (2x, 3x^2) is (x^2, x^3) + C.