Set 3 Problem number 7

An object with mass 18 kilograms is initially at rest.

What will be its acceleration when acted upon by a net force of 50 Newtons?
What speed will be attained in 7 seconds as a result of this force?

Solution

The first question is asking for the rate at which velocity increases, which is a=F/m=( 50 Newtons)/( 18 Kg)= 2.777778 meters per second per second.

Changing by 2.777778 meters per second every second, in 7 seconds the increase will be ( 7 sec)( 2.777778 m/sec/sec) = 19.44444 m/s.
Since the object started from rest, this will also be its velocity after 7 seconds.

Generalized Solution

The rate at which velocity changes, or the acceleration, is a = F / m.

During a time interval `dt, the velocity will therefore change by a `dv = (F / m) `dt.
If the object starts from rest its final velocity will therefore be

final velocity from rest = vf = 0 + `dv = (F / m) `dt.

Explanation in terms of Figure(s), Extension

The first figure below depicts a 'flow' triangle for an object of mass m subjected to a force F.

The relationship a = F / m can be understood as saying that greater force implies proportionally greater acceleration for a given mass while greater mass implies proportionally less acceleration for a given force.
The relationship F = m * a can be understood as saying that

to achieve a given acceleration a greater force must be exerted on a greater mass and that

for a given mass a greater acceleration will require a greater force.

The relationship m = F / a tells us that for a given observed acceleration the greater the force the greater the mass being accelerated, and for a given applied force a greater acceleration implies that less mass is being accelerated.

The second figure depicts a 'flow' diagram for an object of mass m, initially with velocity v0, subjected to a force F for time interval `dt.

From the force and the mass we deduce the acceleration (the 'blue' triangle).
From the acceleration and the time interval we deduce the change `dv in velocity (the 'green' triangle).
From the change in velocity and initial velocity we obtain the final velocity (the 'purple' triangle).