Hey! I know I've had a lot of questions on here over the past couple days, but I am just ensuring I understand what I am doing, and you guys do such a great job of explaining everything!
Okay, I have a derivative question that I am not entirely sure how to solve, so I was hoping you guys could help me out!
The position function of an object moving along a straight line is given by the function , where s is in metres and t s in seconds and .
i) When is the velocity the object greater than 21 m/s?
ii) When is the speed of the object less than 21 m/s?
I really have no idea how to solve for this! With the equation given I know the distance in metres after t seconds, but not the velocity, and the question is asking for velocity.
How would I go about solving this question?
Speed is the rate of change of distance with time.
Velocity is the rate of change of displacement with time.
Speed is the first derivative of distance with respect to time.
Velocity is the first derivative of displacement with respect to time.
Let me clarify.
v(t)=s'(t), that is the instantaneous velocity at time t.
Velocity is speed with direction, and speed is velocity with no direction, so the speed equals |v(t)| or |s'(t)|.
What she needs to find is: