Question

A body falls from rest. Its velocity at the end of first second is: $\left( {g = 32\,ft{{\sec }^{ - 1}}} \right)$
A) $16\,ft{\sec ^{ - 1}}$
B) $32\,ft{\sec ^{ - 1}}$
C) $64\,ft{\sec ^{ - 1}}$
D) $24\,ft{\sec ^{ - 1}}$

Answer 1

Hint: Use the formula of the newton’s law of motion, and substitute the value of the initial velocity, time and the acceleration due to gravity in it. The simplification of this value provides the final velocity of the body which falls from the rest.

Formula used:
The newton’s law of motion is given as
$v = u + at$
Where $v$ is the final velocity, $u$ is the initial velocity of the body, $a$ is the acceleration and $t$ is the time taken for the acceleration.

Complete step by step solution:
It is given that
The acceleration of the body, $a = 32\,ft{\sec ^{ - 1}}$
By taking the equation of the motion,
$v = u + at$
Since at first, the ball is in rest condition, the initial velocity of the body is zero. The time is taken as $1$, since the velocity is to be found after one second. And the acceleration is taken as the acceleration due to gravity, since the body falls down. Substituting the known values in the above equation
$\Rightarrow$ $v = 0 + 32 \times 1$
By simplifying the above equation, we get the following result.
$\Rightarrow$ $v = 32\,ft{\sec ^{ - 1}}$
Thus the velocity of the body which falls from the rest is obtained as $32\,ft{\sec ^{ - 1}}$.

Thus the option (B) is correct.

Note: Here, in this question no external force is provided to the body and also the body does not move by itself. It moves by the force of the gravity and hence the acceleration is taken as the acceleration due to gravity and substituted.