You drive with a constant speed of 15.1 m/s for 23.4 s. You then accelerate for 28.7 s to a speed of 25.8 m/s. You then slow to a stop in 37.1 s. How far have you traveled?

I've tried dividing this into 3 parts.
1st- constant speed
15.1m/s*23.4s=353.34 m

2nd-accelerating
I solved for acceleration, v=v0+at, a=0.0836 m/s^2, then plugged into x=x0+v0t+(1/2)at^2 where x=0+(23.4m/s)(28.7s)+(1/2)(.0836m/s^2)(28.7)^2=706.35

353.34+706.35=1059.35

I'm stuck after this. What do I do with the negative acceleration for the last part? I appreciate any guidance.

ok on first leg.

Second leg, accelerating;
distance= average velocity*time
= 1/2 (15.1+28.7)*25.8

third leg:
distance= avg velocity*time
= 1/2 (28.7+0)*37.1

That isn't correct. Any other thoughts on this problem?

Nevermind, you just accidentally switched the velocity and time. It's (1/2)(15.1+25.8)*(28.7) and (1/2)(25.8)*37.1. Thank you so much for your help! I can't believe I didn't see that before.

To calculate the distance traveled during the deceleration phase, we can use the equation x = x0 + v0t + (1/2)at^2, where x is the distance traveled, x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.

In this case, during the last part of the motion where you slow to a stop, the initial velocity is 25.8 m/s, the acceleration is negative (because it's a deceleration), and the time is 37.1 s. Since you're slowing down to a stop, the final velocity (vf) is 0 m/s.

To find the acceleration during this phase, we can use the equation vf = v0 + at, where vf is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we can solve for the acceleration:

0 m/s = 25.8 m/s + a * 37.1 s

Solving for a, we get:
a = -25.8 m/s / 37.1 s
a ≈ -0.696 m/s^2

Now, we can calculate the distance traveled during the deceleration phase using the equation x = x0 + v0t + (1/2)at^2:

x = 0 + 25.8 m/s * 37.1 s + (1/2) * (-0.696 m/s^2) * (37.1 s)^2
x ≈ 478.8698 m

Therefore, the total distance traveled is the sum of the distances from each phase:

Total distance = 353.34 m + 706.35 m + 478.8698 m
Total distance ≈ 1538.5598 m

Thus, you have traveled approximately 1538.56 meters.