If the equation describing the motion of a rocket is
x = 10 + 5t^2, write an expression for the instantaneous speed of the rocket. What is the instantaneous speed at 5 s. What is the acceleration?

WHere do I begin? Do I need to take the integral anywhere?

Question

If the equation describing the motion of a rocket is 
x = 10 + 5t^2, write an expression for the instantaneous speed of the rocket. What is the instantaneous speed at 5 s. What is the acceleration?


WHere do I begin? Do I need to take the integral anywhere?

anonymous · Answer

Velocity = Derivative of position, thus the velocity equation here: v(x) = $$(1\div2) * 5t$$

anonymous · Answer

To find velocity after 5 seconds, substitute t with 5 in the newly formed velocity equation

anonymous · Answer

Acceleration is in turn given by the derivative of the velocity

nick67 · Answer

@GerhardV
don't you think that the derivative of the power function is:
$$y=x ^{n} y \prime=nx ^{n-1}$$