Question

A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of $400\,m\,in\,20\sec$ . Find its acceleration. Find the force acting on it if its mass is $7\,metric\,tons$ (Hint: $1\,metric\,ton = 1000\,kg$ )

Answer 1

In order to this question, first we will rewrite the given facts as per the question, and then we will first apply second equation of motion to find the acceleration and then we will apply the Newton’s 2nd law of motion to find the force acts on the truck.

Formula used:
2nd law of motion, i.e.. $s = ut + \dfrac{1}{2}a{t^2}$
And, Newton’s second law of motion: $F = ma$

Complete answer:
Given that: the truck starts from rest, so initial velocity, $u = 0$.
And, the distance is given, $s = 400\,m$.
The time taken to cover the given distance, $t = 20\sec$.
Mass of the truck, $m = 7metric\,tons = 7 \times 1000\,kg = 7000\,kg$.
Now, to find the acceleration by which the truck covered $400\,m\,in\,20\sec$,we will go through the 2nd equation of motion-
Now, by applying second equation of motion:-
$\because s = ut + \dfrac{1}{2}a{t^2} \\\ \Rightarrow 400 = 0 \times 20 + \dfrac{1}{2} \times a \times {(20)^2} \\\ \Rightarrow 400 = 20a \\\ \Rightarrow a = 2m.{s^{ - 2}} \\\$
Hence, the required acceleration is $2m.{s^{ - 2}}$.Now, to find the force acts on it, we will apply Newton’s 2nd law of motion:-
$F = m \times a \\\ \Rightarrow F = 7000 \times 2 \\\ \therefore F = 14000N\,or\,1.4 \times {10^4}N \\\$
Hence, the required force that acts on the truck is $1.4 \times {10^4}\,N$.

Note: The link between the force and acceleration of any object in the universe is described by Isaac Newton's second law of motion. The following is a statement based on this postulate: The rate of change in momentum of an object is proportional to the applied unbalanced force in the direction of the force, according to this hypothesis.