Question

What will be the speed of the vehicle when a force of $1000N$ is applied for $10$ second? The mass of the vehicle is $1000kg$ and its speed is $10m/\sec $.
A) $20m/s$
B) $10m/s$
C) $25m/s$
D) $1.5m/s$

Answer 1

-Hint: - First of all, we have to find the acceleration of the vehicle. So, we have to use Newton’s Second law of motion which can be expressed as-
$F = ma$
Now, use the first equation of motion which is –
$v = u + at$

Complete Step by Step Solution: -
Let the force applied on the vehicle be $F$, mass of vehicle be $m$ and acceleration of vehicle be $a.$
According to the question, it is given that
$F = 1000N$
$
  m = 1000kg \\
  a = ? \\
 $
Now, we will use Newton's Second law for determining the acceleration of the vehicle.
There are three laws of Newton but we need only Newton’s second law. Mathematically, Newton’s second law can be represented as -
$F = ma \cdots (1)$
Now, putting the values of force and mass in their respective places in equation $(1)$
$
  1000 = 1000 \times a \\
   \Rightarrow a = 1m{s^{ - 2}} \\
 $
The acceleration produced by vehicle is $1m/{\sec ^2}$.
Now, we have to find the speed of vehicle after the force is applied
So, we have to find out the final speed of the vehicle.
Therefore, let the final speed of vehicle be $v$, initial speed be $u$ and time be $t.$
From the question, it is given that –
$
  t = 10\sec \\
  u = 10m/\sec \\
 $
So, by using the second equation of motion we can calculate the final speed of vehicle which can be expressed as-
$v = u + at$
Putting the values from question
$
  v = 10 + 1 \times 10 \\
  v = 20m/\sec \\
 $
Therefore, the speed of the vehicle after the force is applied is $20m/\sec $.

So, option (A) is correct.

Note: - Newton’s second law states that the net force acting on an object is equal to product of mass of an object and acceleration produced by object.