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!
Question
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?
Question
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?
@pickslides
Speed is the rate of change of distance with time.
Velocity is the rate of change of displacement with time.
which means:
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:
i) s'(t)>21
ii)|s'(t)|<21