The acceleration of a race car during the first 35 seconds of a road test is modeled as

a(t) = 0.024t²1.68t+22.66ft/sec² wheretis the number of seconds since the test began.

Assume that velocity and distance were both 0 at the beginning of the road test. (Hint:ft/sec²can be thought of asft/secper second.)

(a) What was the average acceleration during the first 35 seconds of the road test?

(blank) ft/sec²

(b) What was the average velocity during the first 35 seconds of the road test?

(blank) ft/sec

(c) How far did the race car travel during the first 35 seconds of the road test?

(blank)ft

(d) If the car had been traveling at its average velocity throughout the 35 seconds, how far would the car have traveled during those35 seconds?

(blank) ft

Please fill in the blanks and state answers clearly!