Question

a student is learning about gravitation by dropping a marble from a tower on earth, and measuring the results with a stopwatch, a speedometer, and a tape measure.
time (s) speed (m/s) distance (m)
0.0 0.0 0.0
1.0 10 5
2.0 20 20
3.0 30 45
4.0 40 80
what is the marbles acceleration?
m/s²
if the marble were dropped from a very tall building, what would its speed be after a time of 7.0s?
70 m/s
if the marble were dropped from a very tall building, how far would it travel in a time of 7.0s?
m

Explanation:

Step1: Find acceleration

Acceleration $a=\frac{\Delta v}{\Delta t}$. Taking two - points, say $t = 0\ s,v = 0\ m/s$ and $t = 1\ s,v = 10\ m/s$. Then $a=\frac{10 - 0}{1-0}=10\ m/s^{2}$.

Step2: Find distance traveled in 7s

The formula for the distance traveled by an object in free - fall is $d=\frac{1}{2}at^{2}$, where $a = 10\ m/s^{2}$ and $t = 7\ s$. Substitute the values: $d=\frac{1}{2}\times10\times7^{2}=245\ m$.

Answer:

The marble's acceleration is $10\ m/s^{2}$.
The distance traveled in 7.0s is $245\ m$.