Question

An automobile vehicle has a mass of \[1500kg\]. What must be the force between the vehicle and the road if the vehicle is to be stopped with a negative acceleration of \[1.7\dfrac{m}{{{s^2}}}\]?

Answer 1

Hint: The Following problem is solved using Newton’s Second law of motion. The Second Law states that force is equal to the rate of change of momentum and also for a constant mass, force equals mass times acceleration. The magnitude of the net force is directionally proportional to the acceleration of an object. The same direction is the net force, inversely proportional to the mass of the object.

Formula used:
 Newton’s Second law of motion
\[Force = Mass \times Acceleration\]


Complete answer:
Given:
Mass of the automobile vehicle, \[m = 1500kg\]
Final velocity, \[v = 0\] (finally the automobile stops)
Acceleration of the automobile, \[a = 1.7\dfrac{m}{{{s^2}}}\]
Find out:
To find if the vehicle is to be stopped with a negative acceleration of \[1.7\dfrac{m}{{{s^2}}}\]when the force between the vehicle and the road.
Using Newton’s second law of motion formula to find a solution.
\[Force = Mass \times Acceleration\]
\[F = 1500 \times \left( { - 1.7} \right)\]
\[ = - 2550N\]
Therefore, the force between the automobile and the road is \[2550N\], in the opposite direction of the automobile’s motion.

Note: The applications of the second law can be seen in identifying the amount of force needed to make an object move or to make it stop.
We kick a ball when we exert force in a specific direction, which is the direction in which it will travel. As the stronger the ball is kicked, the stronger the force we put on it, and the further away it will travel.