# Math Help - Displacement and Distance of a Velocity function

1. ## Displacement and Distance of a Velocity function

I'm unsure or not if the anti derivative of this would be displacement, in fact i'm unsure of how to even tackle this. Please help me, I'm clueless!

3. v(t) = t^3 -5t^2 +6t
a) determine displacement over the interval 0-5
b) determine total distance over the interval 0-5

2. Originally Posted by Lupus7874
I'm unsure or not if the anti derivative of this would be displacement, in fact i'm unsure of how to even tackle this. Please help me, I'm clueless!

3. v(t) = t^3 -5t^2 +6t
a) determine displacement over the interval 0-5
b) determine total distance over the interval 0-5
a) $\frac{dx}{dt} = v$ therefore ....

b) Start by drawing a graph of x versus t.

Your textbook and/or class notes should contain examples to follow ....

3. a) So the antiderivative would be displacement assuming I calculated for t=5? that feels too simple but thats the only answer I'm coming up with.

as for example b) i've sketched the graph of velocity (should I be sketching position?) roughly by plugging in values of t, but I don't think I'm getting the right answer as setting the equation equal to 0 provides me with the information that there is negative velocity somewhere in there, can anyone help me with the proper method?