Physics, asked by amanakp, 1 year ago


8
the distance X moved by a body of mass 0.5 kg
under the action of a force varies with time t as
vm) = 3t²+ 4t + 5 (here t is expresed in second)
What is the work done by the force in first
2 seconds?
(2) 40 J
(3) 50 J
(4) 60 J
(1) 20 J​

Answers

Answered by Anonymous
37

Answer:

Work done = 40 J

Explanation:

Given ;

Mass ( m )  = 0.5 kg

\displaystyle{}v=3t^2+4t+5}\\\\\displaystyle{a=\dfrac{dv}{dt}}\\\\\displaystyle{a=\dfrac{d}{dt}(3t^2+4t+5)}\\\\\displaystyle{a=6t+4}

putting t = 2 sec  we get

a = 6 × 2 + 4

\displaystyle{a=16m/sec^2}

Now from Newton second law of motion

\displaystyle{s = u t + 1 / 2 at^2}

Here u = 0

s = 1 / 2 × 16 × 2 × 2

s = 32 m

Now for work done ;

\displaystyle{W = \vec{F} \ . \vec {s}}

W = 0.5  ×  16  +  32 J

W =  8 + 32 J

W = 40 J

Thus work done is 40 J

Answered by sagarnirapure914
63

Correct question :-

The distance x moved by a body of mass 0.5 kg by a force varies with time t as x = 3t² + 4t + 5, where x is expressed in metres and t in seconds. What is the work done by the force in the first 2 seconds?

Answer :-

Work done = 75 J

Explanation :-

Mass = 0.5 kg

distance = x = 3t² + 4t + 5

_____________________[Given]

We know that,

Acceleration (a) = d²(x)/dt²

=> a = d²(3t² + 4t + 5)/dt²

=> a = 6 m/s²

______________________________

Also,

Force (F) = mass × acceleration

=> F = 0.5 × 6

=> F = 3 N

_______________________________

Now,

Distance travelled = x = 3t² + 4t + 5

Put t = 2 sec , we get

x = 3(2)² + 4(2) + 5

=> x = 12 + 8 + 5

=> x = 25 m

_______________________________

Now,

To find :- Work done = ?

We have,

Work done (W) = Force × distance

=> W = 3 × 25

=> W = 75 J

______________________________

Hence, the work done is 75 J

________________________[Answer]

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