Question

The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle moving along a line. a(t) = 2t 2, v(0) = −3, 0 ≤ t ≤ 4 (a) Find the velocity (in m/s) at time t. v(t) = t2 2t−3 Correct: Your answer is correct. m/s (b) Find the distance traveled (in m) during the given time interval. Incorrect: Your answer is incorrect. m

Answer 1

The distance traveled during the given time interval is 13.67 m.

Step-by-step explanation:

To find the distance traveled during the given time interval, we can integrate the velocity function over that interval. The velocity function is given by v(t) = t^2/2t - 3. Integrating this function over the interval [0, 4] gives:

∫[0, 4] t^2/2t - 3 dt = [t^3/6 - 3t] evaluated from 0 to 4 = (4^3/6 - 3(4)) - (0^3/6 - 3(0)) = (64/6 - 12) - (0 - 0) = 77/3 - 12 = 41/3 = 13.67 m

So, the distance traveled during the given time interval is 13.67 m.