Question

An automobile vehicle has a mass of 1500kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of${\text{ 1}}{\text{.7 m}}{{\text{s}}^{ - 2}}{\text{ }}$?

Answer 1

Hint
When the velocity of a moving body changes we can say that the body is accelerated. The change of velocity with time is defined as acceleration. When the velocity of the body increases we can say that the velocity is positive. When the acceleration is negative, the velocity of the body decreases. Negative acceleration is called retardation.
$\Rightarrow F = ma$ (Where,${\text{ F }}$stands for the force acting on an object, ${\text{ m }}$stands for the mass of the object and ${\text{ a }}$stands for the acceleration of the object)

Complete step by step answer
Newton’s second law of motion states that the force is the product of mass and acceleration.
It is expressed as, ${\text{ }}F = ma$
The mass of the vehicle is given by, ${\text{ m = 1500 kg}}$
It is given that the acceleration is negative.
Acceleration of the body${\text{ a = - 1}}{\text{.7 m}}{{\text{s}}^{ - 2}}$
The force between the vehicle and the road will be,
$\Rightarrow F = ma$
Substituting, ${\text{ m = 1500 kg}}$ and ${\text{ a = - 1}}{\text{.7 m}}{{\text{s}}^{ - 2}}$ we get
$\Rightarrow F = 1500 \times - 1.7$
$\Rightarrow F = - 2550N$
The negative sign signifies that the force is acting against the direction of motion of the body. This is a retarding force.
The answer is: $- 2550N$.

Note:
The force between the moving vehicle and the road is the frictional force. Friction may be defined as the force that opposes the relative motion between two surfaces that are in contact. The frictional force acts tangential to the surface of contact. Frictional force arises due to the adhesive force between the surfaces of two bodies. It can also arise due to the irregularities on the surface of the plane. The friction arising between the surfaces of two bodies that are in contact as long as they are in rest is called static friction. The frictional force between the surfaces of two bodies that are in motion is called kinetic friction. The frictional force has many advantages as well as disadvantages. Frictional force helps us to walk steadily on the ground without slipping. It also helps us to hold objects in our hands. The major disadvantage of frictional force is the loss of energy in moving objects to overcome friction.