Question

Students in science class performed an experiment where they dropped various objects from the same height. They timed how long it took each object to reach the ground. This data is shown in the table below. For each object, calculate the speed and acceleration. Then, make a statement about the results!

Answer 1

The speed of the object can be given as,

`v=(d)/(t)`

Also, the final speed of the object can be expressed as,

`v=u+at`

For marble, the distance covered is 10 m in 1.01 s. Plug in the known values,

`\begin{gathered} v=\frac{10\text{ m}}{1.01\text{ s}} \\ =9.90\text{ m/s} \end{gathered}`

The acceleration can be calculated as,

`\begin{gathered} 9.90\text{ m/s=0 m/s+a(1.01 s)} \\ a=\frac{9.90\text{ m/s}}{1.01\text{ s}} \\ =9.80m/s^2 \end{gathered}`

For bowling ball, the distance covered is 10 m in 1.03 s.

Substitute the known values in the formula of speed.

`\begin{gathered} v=\frac{10\text{ m}}{1.03\text{ s}} \\ \approx9.71\text{ m/s} \end{gathered}`

Plug in the known values in formula of final speed to calculate the acceleration.

`\begin{gathered} 9.71\text{ m/s=0 m/s+a(1.03 s)} \\ a=\frac{9.71\text{ m/s}}{1.03\text{ s}} \\ \approx9.43m/s^2 \end{gathered}`

For baseball the distance covered is 10 m in 0.99 s.

Substitute the known values to calculate the speed of baseball.

`\begin{gathered} v=\frac{10\text{ m}}{0.99\text{ s}} \\ \approx10.1\text{ m/s} \end{gathered}`

Substitute the known values in the expression of final speed to obtain the acceleration.

`\begin{gathered} 10.1\text{ m/s=0 m/s+a(0.99 s)} \\ a=\frac{10.1\text{ m/s}}{0.99\text{ s}} \\ \approx10.2m/s^2 \end{gathered}`

Therefore, the speed and the acceleration of the baseball is maximum which is 10.1 m/s and 10.2 m/s2 respectively, because the time taken by ball to cover the distace is minimum.