Question

If a loaded truck that can accelerate at 2 m/s2 loses its load and has one-third of its original mass, what acceleration can it attain if the same driving force acts on it?

Answer 1

F=ma (original mass)
F=ma (1/3 original mass)

Because you want the same driving force (same F) for both situations, you can set these two equations = to each other.

ma (original mass) = ma (1/3 original mass)

You are given the acceleration of the orginal mass, 2m/s^2.
You know the second situation has 1/3 of the orginal mass.

So (m)*(2m/s^2) = 1/3(m)*(a); because m is on each side they cancel so:

2m/s^2=1/3a Solve for a by multiply the other side by 3.
(2m/s^2)*(3) = a = 6m/s^2

This makes sense because in order to maintain the same magnitude of F, the acceleration would need to make up for the loss of mass.

Answer 2

here,
1st case, acceleration(a)= 2 m/s^2 force=f (say) mass=m (say)
then,
f=ma=mx2=2m......(1)

2nd case
acceleration(a)=a' (say) force=f mass=m/3
then,
f=ma=(m/3)xa'.......(2)

from question force "f" is equal in both the cases.then,
equation 1=equation 2
i.e. 2m=(m/3)xa'
or,a'=(2x3)m/m=6 m/s^2

so,to act same driving force on truck acceleration must be 6 m/s^2 when mass becomes one-third of its original mass.