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 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.

tiburtius | High School Teacher | (Level 2) Educator

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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 ` `

`|int_1^7(t^2-10t+16)dt|=|(t^3/3-5t^2+16t)|_1^7|=`

`|343/3-245+112-1/3+5-16|=|-30|=30`

Notice -30 above, this means the object traveled in negative direction e.g. if up is positive direction, then object was falling/moving down.