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A force of 6.0 N is applied horizontally to a 3.0 kg crate initially at rest on a horizontal frictionless surface. After the crate is pushed for 1.5 seconds, it has a velocity of 3.0 m/s. Does this support Newton's second law of motion, that force equals mass times acceleration? Explain. 

a. Yes, because the acceleration of the crate is 2.0 m/s².

b. No, because the acceleration of the crate is 2.0 m/s².

c. Yes, because the mass and the velocity of the crate are equal.

d. No, because the mass and the velocity of the crate are equal. ​

Respuesta :

MrRoyal

Answer:

a. Yes, because the acceleration of the crate is 2.0 m/s².

Explanation:

Given

[tex]Force = 6N[/tex] --- f

[tex]Mass = 3kg[/tex] --- m

[tex]Time = 1.5s[/tex] --- t

[tex]Velocity = 3.0m/s[/tex] --- v

Required

Does the system support [tex]F=ma[/tex]

Yes, it does and this is shown below

The crate is initially at rest; so:

[tex]u = 0[/tex]

Using the first equation of motion

[tex]v = u + at[/tex]

Substitute values for v, u and t

[tex]3 = 0 + a*1.5[/tex]

[tex]3 = 1.5a[/tex]

Make a the subject

[tex]a = 3/1.5[/tex]

[tex]a = 2[/tex]

Using [tex]F = ma[/tex]

Substitute values for F and m

[tex]6 = 3 * a[/tex]

Divide both sides by 3

[tex]6/3 = 3/3 * a[/tex]

[tex]2 = a[/tex]

[tex]a = 2[/tex]

In both cases:

[tex]a = 2[/tex]

Hence, option (a) is correct.