Nitrate said:Homework Statement
A stone is thrown up at 30 m/s from the edge of a bridge 210 m above the river below. How many seconds elapse between toss and splash?
Homework Equations
The Attempt at a Solution
dv/dt=-9.8
v=-9.8t+c2
30=-9.8(0) + c1
c1=30
v=-9.8t+30
h=-4.9t^2+30t+c2
210=-4.9(0)^2+30(0)+c2
c2=210
h= -4.9t^2+30t+210
i'm not sure if I'm doing this right/what to do next if i am
An antiderivative is the opposite of a derivative. It is a mathematical function that, when differentiated, gives the original function. In terms of motion, an antiderivative represents the displacement of an object over time, while the derivative represents the velocity of the object.
Antiderivatives are used in calculus to find the position and velocity of an object at any given time. By taking the antiderivative of the velocity function, we can find the displacement function, which gives the position of the object over time. And by taking the derivative of the displacement function, we can find the velocity function, which gives the velocity of the object at any given time.
The fundamental theorem of calculus states that the area under a curve can be found by evaluating the antiderivative of the function at the upper and lower bounds of the integral. In terms of motion, this means that the displacement of an object can be found by taking the antiderivative of the velocity function and evaluating it at the initial and final times.
Yes, antiderivatives are used in many real-world applications, including problems related to motion. For example, they can be used to calculate the distance traveled by a moving object, the time it takes to reach a certain position, or the acceleration of an object at a given time.
One common mistake is forgetting to include the constant of integration when calculating the antiderivative. This constant is necessary because the derivative of a constant is always zero, and it can affect the final result of the problem. It is also important to carefully consider the units of the functions and their derivatives when solving real-world problems.