A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 1 2 and t = 1 s? Use Galileo's formula v (t) = - 9.8t m/s.

There is one mistake in the question. The Correct question is here

A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 1/2 and t = 1 s? Use Galileo's formula v (t) = - 9.8t m/s.

Answer:

y (1s) - y (1/2s) = - 3.675 m

The cat falls 3.675 m between time 1/2 s and 1 s.

Explanation:

Given data

time=1/2 sec to 1 sec

v (t) = -9.8t m/s

To find

Distance

Solution

As the acceleration as first derivative of velocity with respect to time

So

acceleration (-g) = dv/dt

Solve it

dv = a dt

dv = - g dt

v - v₀ = - gt

v = dy/dt

dy = v dt

dy = (v₀ - gt) dt

y (1s) - y (1/2s) = (v₀) (1 - 1/2) - (g/2) [ (t1) ² - (t1/2s) ² ]

y (1s) - y (1/2s) = ( - 9.8/2) [ (1) ² - (1/2) ² ]

y1s - y1/2s = ( - 4.9 m/s²) (3/4 s²)

y (1s) - y (1/2s) = - 3.675 m

The cat falls 3.675 m between time 1/2 s and 1 s.