A body of mass 4 kg is accelerated from rest by a steady force of 9N. What is its speed when it has travelled a distance of 8m?
6 ms-1
18 ms-1
32 ms-1
36 ms-1
48 ms-1
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There are two parts to this question:
Newton’s second law and the
equations of motion.
Using Newton’s second law:
F=ma
a=F/m
so a=9/4ms^-2
Using equations of motion:
The question states that it wants the
speed at 5m so this implies that you
want the final velocity rather than the
initial velocity. Also it is accelerated
“from rest” so this implies that the
initial velocity is 0.
s=8
u=0
v=?
a=9/4 (calculated in part 1)
Now use the equation of motion
v^2=u^2+2as.
Since u=0:
v^2=2as
And then v = square root ( 2as )
Finally, putting your numbers in:
square root ( 2*9/4*8) = 6ms^-1
acceleration=force/mass
=9/4=2.25
then use the third equation of motion
since u=0
v=√0+2*2.25*2
=6m/s
From the Parameters given
M=4kg
F= 9N ; S (distance) = 8m
And V (Speed) = ?
Since V² = u² + 2as ....... from eqn of motion
a (acceleration) can be gotten from
F = ma
Where m = mass
f = force and a = Acceleration Therefore we can make a the subject of formular by saying a = f/m = ( 9/4) = 2.25
Substituting the Value of a into the formula ;; Note u = 0 (because the body is accelerated from rest)
V² = u² + 2as
V² = 2as
V² = 2 X 2.25 X 8
V² = 36
Take the square of both sides
V = √36
V=6m/s
