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.
Assuming an ideal gas, the speed of sound depends on temperature
only. Air is almost an ideal gas.
Assuming the temperature of 25°C in a "standard atmosphere", the
density of air is 1.1644 kg/m3, and the speed of sound is 346.13 m/s.
The velocity can't be specified, since the question gives no information
regarding the direction of the sound.
Answer:
θ = (7π / 3) rad
Explanation:
given,
displacement of simple harmonic motion along x-axis
equation is given as
x = 5 sin (π t + π/3 )
general equation of simple harmonic motion
x = A sin θ
θ is the phase angle
θ = π t + π/3
at t = 2 s


Phase of the motion at t =2 s is θ = (7π / 3) rad
Explanation:
The distance that a car travels down the interstate can be calculated with the following formula:
Distance = Speed x Time
(A) Speed of the car, v = 70 miles per hour = 31.29 m/s
Time, d = 6 hours = 21600 s
Distance = Speed x Time
D = 31.29 m/s × 21600 s
D = 675864 meters
or

(b) Time, d = 10 hours = 36000 s
Distance = Speed x Time
D = 31.29 m/s × 36000 s
D = 1126440 meters
or

(c) Time, d = 15 hours = 54000 s
Distance = Speed x Time
D = 31.29 m/s × 54000 s
D = 1689660 meters
or

Hence, this is the required solution.