Physics Help?

Question

I've tried to work them out and answer them.
I don't seem to get the correct answers. Please help.

1) During a hard sneeze, your eyes might shut for 0.42 s. If you are driving a car at 78 km/h during such a sneeze, how far does the car move during that time?

2) In 1 km races, runner 1 on track 1 (with time 2 min, 39.18 s) appears to be faster than runner 2 on track 2 (2 min, 39.25 s). However, length L2 of track 2 might be slightly greater than length L1 of track 1. How large can L2 - L1 be for us to conclude that runner 1 is faster?

3) A particle's position is given by x = 18.0 - 15.0000000000000000t + 3t2, in which x is in meters and t is in seconds. Where is the particle when it momentarily stops?

4) At a certain time a particle had a speed of 14 m/s in the positive x direction, and 6.8 s later its speed was 85 m/s in the opposite direction. What was the average acceleration of the particle during this 6.8 s interval?

Answer 1

1) D = rt
D = (78km/h)(1h/3600s)(1000m/km)(0.42s) = 9.1m
(Note: All units cancel out except m.)

2)Assume the two runners are the same speed.
Runner 1 time: 120 + 39.18 = 159.18min.
Runner 2 time: 120 + 39.25 = 159.25min.
Difference in time: .25 - .18 = 0.07s
If runner 1 ran exactly 1 km.:
Δs = Δt(r) = Δt(d/t) = (0.07s)(1000m/159.18s) = 0.43975m
If runner 2 ran exactly 1 km.:
Δs = Δt(r) = Δt(d/t) = (0.07s)(1000m/159.25s) = 0.43956m

3) Take the derivative and set it equal to zero:
-15.00 + 6t = 0
6t = -15.00
t = 2.5s
x = 18.0 - 15t + 3t^2
x = 18.0 - 15(2.5) + 3(2.5)^2
x = -0.75m

4) a = Δv/t
a =[ v(terminal) - v(initial)]/t
a = (-85 - 14)/6.8
a = -14.56m/s^2

Answer 2

These are all kinda 'horse sense' types of questions, but I'll show you how to work out the 1'st one and leave the rest to you.

If you're traveling at 78 km.hr, how many meters per second is that?
78 km/hr = 78000 m/hr = 78000 m/3600 s (there are 60 minutes times 60 seconds/minute = 3600 seconds in an hour). Divide to get
78000 m / 3600 s = 21.666 m/s. So now, it .42 seconds you will travel .42 s * 21.666 m/s = 9.0997 or about 9.1 meters.

It's tough at first, but you **have** to think about the units involved in the problem. Keeping track of the units attached to the numbers is the real 'trick' in physics. All it takes is practice ☺

Doug