Question

A truck starts from rest and rolls down a hill with constant acceleration. It travels a distance of 400m in 20s. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes.

Answer 1

Hint
Here, distance, time and initial velocity is given so we can use the Newton’s equation of motion i.e. $s = ut + \dfrac{1}{2}a{t^2}$from this we can find the value of acceleration. Now for calculating force we use Newton’s second law of motion i.e. $F = ma$by using 1 metric tonnes = 1000kg.

Complete step by step answer
Here, it is given that
A truck starts from rest and covers a distance of 400m in 20s.
It means, initial velocity $u = 0$
Distance $s = 400m$
Time $t = 20s$
Now for calculating the value of acceleration, we use Newton’s equation of motion i.e.
$\Rightarrow s = ut + \dfrac{1}{2}a{t^2}$
Now, substitute the values of u, s, and t, we get
$\Rightarrow 400 = 0 + \dfrac{1}{2}a{\left( {20} \right)^2}$
$\Rightarrow a = \dfrac{{400 \times 2}}{{400}} = 2m{s^{ - 2}}$
This is the required value of the acceleration of the truck.
Now for calculating the force acting on it when mass is 7 metric tonnes.
For this we use Newton’s second law of motion i.e. $F = ma$
m is the mass on which force is acting and a is the acceleration.
As mass m = 7 metric tonnes, so we have to convert it in kg. for this we know that
1 metric tonnes = 1000kg
Therefore, 7 metric tonnes = 7000kg
Now substitute the values in Newton’s second law, we get
$\Rightarrow F = 7000 \times 2 = 14000N$
Hence, 14000N force is acting on the mass of 7 metric tonnes.

Note
For these types of questions, we use Newton’s three equation of motion i.e. $s = ut + \dfrac{1}{2}a{t^2}$, $v = u + at$ and ${v^2} - {u^2} = 2as$. Which equation is used will depend upon the given conditions of the questions, here v is the final velocity of the object and u is the initial velocity of the object, s is the distance travelled by the object in t seconds with acceleration a.
Care must be taken in using the units. For example, in the above case mass is always taken in kg but it is given in metric tonnes, so we must convert metric tonnes into kg by using the formula 1 metric tonnes = 1000kg.