Question

How do you convert acceleration to velocity?

Answer 1

Hint: In physics acceleration is represented as the rate of change of velocity of an object. Both speed up or slow down describe the acceleration. When the object speeds up acceleration is taken as positive and if it slows down it is taken as negative. As we know the acceleration is the change of velocity by unit time.

Formula used:
The formula of acceleration \[a = \dfrac{{change{\text{ }}of{\text{ }}velocity\;\;}}{{time{\text{ }}taken\;\;}}\]

Complete step by step answer: Velocity is defined as the rate of change of the object’s position over time. Velocity can be calculated in three different ways.
The first one relies on the basic velocity definition. Which is based on changing the position of an object over time:
\[v = \dfrac{d}{t}\]
The second method is based on the change of velocity caused by acceleration over a specific time interval.
Final velocity \[v = u + at\]
$u$ Is the initial velocity, $t$ is the time.
 The third method is the use of the average velocity formula, which analyzes various velocities over different distances.
Average velocity \[ = {v_1}{t_1} + {v_2}{t_2} + ...\]
We can calculate the reached velocity after accelerating a few seconds, by multiplying the acceleration with the number of seconds that were accelerated.
Let, the reached velocity is \[v\], and the time taken is \[t\]. (where the initial velocity must be zero)
So, to convert acceleration to velocity we can use the formula. Velocity \[v = a \times t\]

Note: The SI unit of velocity is \[m/s\]. And the SI unit of acceleration is \[m/{s^2}\].
Acceleration is a vector quality as it is known as the time rate of change of velocity which is a vector quantity.
There is another method to calculate the velocity function from the acceleration function and the position function from the velocity function. By using integral calculus.
The Fundamental Theorem of Calculus is,
\[\int\limits_{{t_1}}^{{t_2}} {a\left( t \right)} dt = v\left( t \right)_{{t_1}}^{{t_2}} = v\left( {{t_1}} \right) - v({t_2})\].