Question

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. ​

Answer 1

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

Step-by-step explanation:

Given

`Force = 6N` --- f

`Mass = 3kg` --- m

`Time = 1.5s` --- t

`Velocity = 3.0m/s` --- v

Required

Does the system support
`F=ma`

Yes, it does and this is shown below

The crate is initially at rest; so:

`u = 0`

Using the first equation of motion

`v = u + at`

Substitute values for v, u and t

`3 = 0 + a*1.5`

`3 = 1.5a`

Make a the subject

`a = 3/1.5`

`a = 2`

Using
`F = ma`

Substitute values for F and m

`6 = 3 * a`

Divide both sides by 3

`6/3 = 3/3 * a`

`2 = a`

`a = 2`

In both cases:

`a = 2`

Hence, option (a) is correct.