Help with Physics Problems..?

Question

Can somebody help me with these problems? Totally confused.
First it says, "Useful Formula: v = (Triangle)s / (triangle)t
I dont know what the triangle means either.. Then the questions.


1. A car drives down the road 4km in .10 hours. What is its velocity in meters per second?

2. A skater has a velocity of 10.0 m/s. How much time will it take for the skater to go 200.0 m?

3. It takes light a time of 8.3 minutes to travel from the sun to the Earth. If the velocity of light is 3.00 x 10^8 m/s, what is the distance from the Earth to the sun.

4. A pitcher throws a fastball at 160 km/hr. How much time will it take to reach the plate just 18.4m away?

Please provide explanations if you intend to answer! MUCH APPRECIATED!

Answer 1

First of all the triangle means "delta" which basically means change. So the equation is saying that the velocity equals the change in displacement (s) (you can think of this as distance for these problems) over the change in time. I think by velocity they mean average velocity as well.

So for the four problems, you simply use the formula. You can rewrite it to say s=vt, or to say t=s/v, but they are still solvable other wise.

Don't forget to convert km to meters and hours to seconds!

1) v= 4000m/360sec = 11/12 m/sec

2) 10m/sec=200m/t t= 20 sec

3) 3 x 10^8m/sec= s/498 sec s= 1.494 x 10^11 meters

4) 44.45 m/sec= 18.4m/t t= 817 sec

I hoped that helped, and you should double check my answers just in case I did my math wrong.

Answer 2

The triangle Δ (pronounce Delta) means a difference. Δs means a difference between 2 distances: Δs=s2-s1

1) 4km in 10 h =>
speed (v)= s (distance) / t(time) =
= 4km/10h = 0.4 km/h = 400 m/h

1 hour = 3600 sec =>
400 m / h = 400m / 3600 s = 4/36 = 1/9 m/s = 0.111 m/s

2) s = v * t =>
t = s / v = 200 / 10 = 20 s

3) v = 3 * 10^8 * 3600 = 1.08 * 10^12 km/h
t = 8.3 min = 8.3 * 60 = 498 sec => 498 / 3600 = 0,13833 h.
s = v * t = 1.08 * 10^12 * 0,13833 = 149.4 * 10^9 km

4) v = 160km/h = 160 * 10^3 m / 3.6 * 10^3 s= 160 / 6.3 = 44.44 m/s
s = 18.4 m

t = s / v = 18.4 / 44.44 = 0.414 s

Answer 3

The symbol that looks like a triangle is an incremental change. The Greek letter delta.So the formula you have shown: v = (Triangle)s / (triangle)t is just saying that velocity is equal to a change in distance(s) divided by a change in time(t). For the purpose of these four problems you can write this formula as:
velocity = distance / time or (v = d/t)
This formula can be rearranged depending on what variable you're looking for. If you're looking for distance, write d = vt.
If you're looking for time, write t = d/v

1.) v = d/t = 4/ 0.01 = 40km/h(1000m/1km)(1h/3600s) = 11.11m/s
2.) t = d/ v = 200.0/10.0 = 20.0s
3.) d = vt = (3.00 x 10^8)(8.3)(60) = 1.494 x 10^11m
4.) 160km/hr = (160km/hr)(1000m/1km)(1hr/3600s) = 44.44m/s
t = d/v = (18.4)/(44.44) = .414s