Question

A constant force of 2.5 N to the right acts on a 4.5 kg mass for 0.90 s.

(a) Find the final velocity of the mass if it is initially at rest.
. m/s to the right
(b) Find the final velocity of the mass if it is initially moving along the x-axis with a velocity of 11.5 m/s to the left.
. m/s to the left

Answer 1

(a)
`v_f=0.5(m)/(s)`

(b)
`v_f=-11(m)/(s)`

Step-by-step explanation:

(a) Since a constant external force is applied to the body, it is under an uniformly accelerated motion. Using the following kinematic equation, we calculate the final velocity of the mass if it is initially at rest(
`v_0=0`):

`v_f=v_0+at\\v_f=at(1)`

According to Newton's second law:

`F=ma\\a=(F)/(m)(2)`

Replacing (2) in (1):

`v_f=(F)/(m)t\\v_f=(2.5N)/(4.5kg)(0.9s)\\v_f=0.5(m)/(s)`

(b) In this case we have
`v_0=-11.5(m)/(s)`. So, we use the final velocity equation:

`v_f=v_0+at\\v_f=v_0+(F)/(m)t\\v_f=-11.5(m)/(s)+(2.5N)/(4.5kg)(0.9s)\\v_f=-11(m)/(s)`