Question

When a force of 1 newton acts on a mass of 1 kg that is able to move freely, the object moves with a(n):
(A) Speed of $1m{s^{ - 1}}$
(B) Acceleration of $1m{s^{ - 2}}$
(C) Speed of $1 km{s^{ - 1}}$
(D) None of these

Answer 1

Relation between force, mass and acceleration. Mass is defined as the amount of matter present in it and acceleration is the change in velocity per unit time.

Formula Used:
F = ma
Here, F= Force acting on a body
m=mass of the body
a= acceleration acting on the body

Complete step by step answer:
Force is defined as the product of mass and acceleration i.e. F = ma where F is force, m is mass and a is acceleration. This relation is being derived from Newton's second law of motion. One newton is that force which when acting on a body of mass 1 kg, produces an acceleration of $1m{s^{ - 2}}$.
Numerically, F = 1 N [ N is the symbol of Newton], m = 1 kg
$F = ma$
Now, We will put the values in the given formula
$1N = 1kg \times a$
$a = \dfrac{{1N}}{{1kg}}$
$a = \dfrac{{1 kg m{s^{ - 2}}}}{{1kg}}$
$a = 1m{s^{ - 2}}$
Hence, option (B) is correct.

Additional information:
$F = ma$ is Newton’s second law only in a special case when mass m of the body is constant at velocity v (which is much smaller than the velocity of light c). But its second law in the form F is equal to Change in momentum divided by change in time is true in all situations and thus it is one of the fundamental laws of Physics.

Note: Both force and acceleration are vector quantities. The acceleration is positive as it is in the direction of force. When a force of 1 N is applied on a body of mass 1 kg, acceleration is $1m{s^{ - 1}}$.