how far does car move if...?

Question

A coasting cart has velocities 1.5 m/s, 4 m/s and 11.75 m/s at clock times t = 0 s, 3 s and 6 s. Approximately how far does it move and at what average rate does it accelerate over each of the two time intervals (i.e., 0- 3 seconds and 3 - 6 seconds)?

If the automobile is coasting, and if air resistance is not a significant factor, then over which time interval do you think the average slope of the road is greatest?

Answer 1

I have no clue, maybe my seventh grader can help, she has an aptitude for math, but she didn't get it from me :)

Good Luck!!!

Answer 2

The average acceleration of an object is the change in velocity, divided by the time interval.

So, the average acceleration during the first interval is:
a = (4 m/s - 1.5 m/s) / (3 s)
a = (2.5 m/s) / (3 s)
a = 0.833 m/s^2

The average acceleration during the second interval is:
a = (11.75 m/s - 4 m/s) / (3 s)
a = (7.75 m/s) / (3 s)
a = 2.58 m/s^2

The acceleration is greater during the second interval, so if the car was coasting, you'd expect the slope of the road to be higher during this interval.