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Alina [70]
3 years ago
11

a 3.5 kg mass has an initial velocity of 4.0 m/s. How much force is required to increase the velocity of the mass to 8.0 m/s in

3.0 seconds?
Physics
1 answer:
Nadya [2.5K]3 years ago
6 0

Answer:

<em>4.67 N of force are required</em>

Explanation:

The second Newton's law states the net force exerted on a body of mass m that has an acceleration a, is given by:

F=m.a

On the other hand, the kinematics equations relate the acceleration with the change of speed over time, expressed as:

\displaystyle a=\frac{v_f-v_o}{t}

We are given the initial speed of vo=4 m/s on a mass of m=3.5 Kg, the final speed of vf=8 m/s which took t=3 seconds.

The acceleration is:

\displaystyle a=\frac{8-4}{3}=1.33

a=1.33\ m/s^2

Thus, the force is:

F=3.5\ Kg\cdot 1.33\ m/s^2

F=4.67\ N

4.67 N of force are required

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x_{f}-x_{i}=v_{i}t+(1/2)at^{2}\\  -5.0m=(o)t+(1/2)(-9.8m/s^{2} )t^{2}\\ -4.9t^{2}=-5.0\\ t^{2}=5/4.9\\t=\sqrt{1.02} \\t=1.01s

As we have find the time taken now we need to find the final velocity vf from below equation as

v_{f}=v_{i}+at\\v_{f}=0+(-9.8m/s^{2} )(1.01s) \\v_{f}=-9.898m/s

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first we need to find total time as

t=3.0-1.01 =1.99 s

|D_{depth} |=|vt|\\|D_{depth} |=|(-9.898m/s)(1.99s)|\\|D_{depth} |=19.697m

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Answer:

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