Question

At time t, the position of a body moving along the s-axis is s = t³-9t2+ 24t. Find the total distance traveled by the body from t = 0 to t = 3.

A 54 m
B 38 m
C 18 m
D 22 m

Answer 1

D. 22 m

Explanation:

A curved position vs. time graph means the object is accelerating. If you plot this equation, you can see that from t=0 to t=2, the object traveled from the origin to a position 20 m away. Or you can set t=2 and solve the equation for s and get s=20.

At t=3, s = 18

s = 3³ - 9(3²) + 24(3) = 18

On the graph of this equation, you can see it curves down from s=20 to s=18 from t=2 to t=3.

So the best approximate answer to the question is D. 22m

The object traveled 20 m during the first 2 seconds, then in the next second changed direction and traveled another 2 m to arrive at 18 m from the origin. Total distance traveled was 20 + 2 = 22 m