The velocity of an object moving along a straight line is v(t)= t^2 – 10t + 16. Find the total distance traveled by the object from the interval [1,7]
The other question in this problem is find the displacement over the time interval [1,7]. But I already found that and it was -30 units. I need help with finding the total distance traveled.
Since by definition `v(t)=s'(t)` it follows that `s(t)=int_0^tv(x)dx.` So to find the distance traveled in interval `[1,7]` you need to calculate `int_1^7v(t)dt.` So your distance traveled `d(1,7)` is ` `
Notice -30 above, this means the object traveled in negative direction e.g. if up is positive direction, then object was falling/moving down.