Nitrate said:Homework Statement
An object moves in a straight line with velocity v = 6t-3t^2, where v is measured in metres per second.
a) how far does the object move in the first sec?
b) how far does the object move in the first two seconds?
c) the object is back where it started when t=3. how far did it travel to get there?Homework Equations
The Attempt at a Solution
the only bit i got was the anti derivative s=3t^2-t^3+c
help is requested :D
Motion is the change in position of an object over time.
Antiderivatives can be used to find the original function from its derivative, which in motion problems, represents the velocity of an object. By finding the antiderivative of the velocity function, we can then determine the position of the object at any given time.
The first step is to identify the function representing the velocity of the object. Then, find its antiderivative to get the function for position. Next, plug in the given time values to determine the positions at those times. Finally, interpret the results in the context of the problem.
Velocity is measured in distance per time, such as meters per second or miles per hour. Position is measured in units of distance, such as meters or miles.
Yes, antiderivatives can only be used for objects with constant acceleration. If the object has varying acceleration, more advanced tools such as the Fundamental Theorem of Calculus may be needed.