Question

How do you find acceleration without time?

Answer 1

Hint: Acceleration is a vector quantity that has both direction and magnitude. Velocity is defined as the distance traveled by an object in a given time. As we have three equations of motion to find the acceleration without time, the third equation will be used because in that equation the value of initial velocity, final velocity, and distance should be known.

Complete step by step answer:
Before going forward, let us know first what is the meaning of acceleration. The rate of change of velocity of an object with respect to time is known as acceleration. The unit of acceleration is given as $${\displaystyle \frac{m}{s^2}}$$. Acceleration can be positive, negative, or zero. Negative acceleration happens when velocity of the object decreases with time. When the velocity of the object increases with time then it is known as positive acceleration and when the velocity of the object remains constant throughout then it is known as zero acceleration.
In physics, we have three equations to motion to find the initial velocity, final velocity, time, acceleration, and distance travelled by the object. So the three equations of motion are given as shown below.
The first equation of motion is
 $$v=u+at$$……. eq(1)
The second equation of motion is
$$s=ut+{\displaystyle \frac{1}{2}}a{t}^2$$….. eq(2)
The third equation of motion is
$$v^2-u^2=2as$$…….. eq(3)
Where ‘v’ is the final velocity, ‘u’ is the initial velocity, ‘a’ is the acceleration and ‘t’ is the time.
 So if we have to find the value of final velocity, initial velocity, time, or the acceleration when the value of time is given then eq(1) will be used. If we have to find the distance travelled by an object when its initial velocity, time taken by the object, or the acceleration then we will use eq(2). Eq(3) will be used if we have to find the acceleration of the object when the time taken by the object is not given but its initial velocity, final velocity, and distance traveled by an object are given.
So, using the equation $$v^2-u^2=2as$$, we can find acceleration without time.

Note:
 An object that is moving in a circular path is still considered accelerating because the speed of the object is constant but its direction is changing continuously. If the acceleration of the object remains constant then it is known as a uniform acceleration and if the acceleration of the object keeps changing then it is known as non-uniform acceleration.