Stuck again. The paper just says that the position of an object is given by s(t)=t^3. When T=5sec find
A. Position
B. Velocity
C. Acceleration
I'm trying to use the "position equation" which is s=1/2 a t^2 = Vot
However, what do I solve the equation for? It seems like none of the variables are given. =/
To solve for the position, velocity, and acceleration at the given time T = 5 seconds, you need to differentiate the position function, s(t) = t^3, with respect to time.
A. Position:
The position of the object at time T is given by s(T) = T^3. Substituting T = 5 seconds into the equation, you get s(5) = 5^3 = 125. So, at T = 5 seconds, the position of the object is 125 units.
B. Velocity:
The velocity of an object is the derivative of the position function with respect to time. By differentiating s(t) = t^3, you get v(t) = 3t^2. To find the velocity at T = 5 seconds, substitute T = 5 seconds into the equation, v(5) = 3(5^2) = 75. The velocity at T = 5 seconds is 75 units per second.
C. Acceleration:
Similarly, the acceleration of an object is the derivative of the velocity function with respect to time. When you differentiate v(t) = 3t^2, you get a(t) = 6t. By substituting T = 5 into the equation, a(5) = 6(5) = 30. The acceleration at T = 5 seconds is 30 units per second squared.
Remember, to find the position, velocity, and acceleration at a specific time, you need to differentiate the position function to find the velocity and differentiate the velocity function to find the acceleration. Then substitute the given time into the respective equations.