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Natali5045456 [20]
3 years ago
7

The acceleration of an object (in m/s2) is given by the function a ( t ) = 7 sin ( t ) . The initial velocity of the object is v

( 0 ) = − 10 m/s. Round your answers to four decimal places.
Physics
1 answer:
jok3333 [9.3K]3 years ago
5 0

Answer:

The answer is "\bold{v(t) = -7 \cos (t) -3}"

Explanation:

Consider the function a(t) = 7 \sin (t)  speed for an Object , and V(0) = -10 \frac{m}{s} is the initial speed of the object.  Find an object-speed v(t) equation:

\to a(t) = 7 \sin(t) \\\\\to v(t) = \int  a(t) dt\\

          = 7 \int \sin (t) dt \\\\= -7 \cos(t) + C

Substituting the  t = 0 in v(t)  

\to v(0) = - 7 \cos(0) + C \\\\\to -10 = -7(1) +C \\\\\to C = -10 +7\\\\\to C= -3

after  substituting the value C:

= - 3 in v(t) = -7 \cos (t) +c  \\\\\to v(t) = -7 \cos(t) -3

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Explanation:

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8 0
3 years ago
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 G
Romashka-Z-Leto [24]

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.

6 0
3 years ago
PLEASE SOMEONE ANSWER!!! thank you so so so much!!!!
Oduvanchick [21]

Answer:

As much I know the gravity on moon is 1.62m/s२.

7 0
3 years ago
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