How fast will an object with a mass of #15 kg# accelerate if a force of # 72 N# is constantly applied to it?

2 Answers
Mar 14, 2018

The acceleration is #4.8 m/s^2#.

Explanation:

The formula that describes the relationship discussed in Newton's 2nd Law is

#F = m*a#.

To find acceleration when knowing force and mass, we need to do some algebra on the above formula. Divide both sides by m and cancel where possible.

#F/m = (cancel(m)*a)/cancel(m)#
So
#a = F/m#

If we plug your data into that equation and perform the indicated division, we find that

#a = F/m = (72 N)/(15 kg) = 4.8 N/(kg)#

The usual units for acceleration are #m/s^2#.
# N/(kg)# does not look so much like acceleration.
But, if we look at #F = m*a# we will see that 1 Newton, applied to a mass of 1 kg, will cause acceleration of 1 m/s^2. So the Newton is equivalent to #(kg*m)/s^2#. That combination of units was named the Newton to honor Isaac.

Therefore,

#a = F/m = 72 N/15 kg = 4.8 N/kg = 4.8 m/s^2#

I hope this helps,
Steve

Mar 15, 2018

#4.8 \ "m/s"^2#

Explanation:

We use Newton's second law of motion here, which states that

#F=ma#

where #m# is the mass of the object in kilograms, #a# is the acceleration of the object in #"m/s"^2#, and #F# is the force acting on the object in newtons.

We need to solve for acceleration, so we can rearrange the equation into

#a=F/m#

Now, plugging in the given values, we get

#a=(72 \ "N")/(15 \ "kg")#

#=4.8 \ "m/s"^2#

So, the object's velocity will keep increasing by #4.8 \ "m/s"# every second towards the direction of the force applied.