Question

How are acceleration, time and velocity related?

Answer 1

Hint: Velocity, acceleration and time are parameters which are used to describe the motion of a body. Velocity is change in displacement with time; acceleration is change in velocity with time. Time is the independent variable and velocity and acceleration are the dependent variables.

Complete answer:
The change in displacement that takes place per second is called velocity. Its SI unit is $m{{s}^{-1}}$. It is given by-
$v=\dfrac{d}{t}$
Here, $v$ is the velocity
$d$ is the displacement
$t$ is time taken
Velocity is also given as-
$v=\dfrac{dx}{dt}$
Here, change in displacement is $dx$, in time $dt$.
Change in velocity in unit time is called acceleration. Its SI unit is $m{{s}^{-2}}$. It is given as-
$a=\dfrac{v-u}{t}$
Here, $a$ is the acceleration
$v$ is the final velocity
$u$ is the initial velocity
$t$ is the time taken
Acceleration can also be given as-
$a=\dfrac{dv}{dt}$
Here, $dv$ is changed in velocity in time $dt$.
From the above equations we can see that velocity is inversely proportional to time taken while acceleration is directly proportional to the change in velocity and inversely proportional to time taken.
The relation between acceleration, velocity and time can also be expressed by the equations of motion in one dimension. They are-
$\begin{align}
  & v=u+at \\
 & {{v}^{2}}={{u}^{2}}+2as \\
 & s=ut+\dfrac{1}{2}a{{t}^{2}} \\
\end{align}$
Here, $v\,and\,u$ are initial and final velocities respectively.
$a$ is the acceleration
$t$ is the time taken
$s$ is the displacement
Therefore, acceleration is directly proportional to change in velocity and both acceleration and velocity are inversely proportional to time.

Note:
Velocity and acceleration are vectors quantities; they have both magnitude as well as direction. By Newton’s second law, acceleration acts on a body if external forces are acting on it. If there are no external forces acting on a body, the body moves with uniform velocity or remains at rest.