The velocity of a particle moving along the x-axis

Question

 

The velocity of a particle moving along the x-axis is v(t) = t² + 2t + 1, with t measured in minutes and v(t) measured in feet per minute. To the nearest foot find the total distance travelled by the particle from t = 0 to t = 2 minutes.

The answer I got is 9 after rounding it to the nearest foot

Answer 1

Hello, Sreeram,

I note that at t = 0, the velocity of the particle is 1 ft/min, not 0. Odd, but true, the equation claims. It's velocity at 2 is 9 feet/min. Then average velocity over the 2 minutes is (1 + 9)/2 = 5 ft/min. Times the 2 minutes between 0 and 2, it travels 10 feet.

I might be wrong, but the equation has this pesky 1 attached to the end. I read that as it has a velocity of 1 from the start.

Bob