Here we are going to discuss how to find the required time to complete a rectilinear motion.

**Object acquires velocity when it change its position with time, and it accelerates when its velocity changes with time. If we know the value of displacement and time, we can find velocity; similarly, we can find acceleration. Now the question arises, How To Find Time With Acceleration And Distance? Mainly, it depends upon the question and quantities given in a question. We can find out the time of linear motion if we have the following three types of data combinations given in a question,**

**Acceleration, as well as the initial and final velocity of an object****velocity and covered distance****speed and acceleration**

**When acceleration, initial velocity, and final velocity are given**

Suppose a question provides a magnitude of acceleration, initial velocity, and final velocity of the object. In that case, the best way to calculate the time required to complete motion is by solving the first kinematical equation of motion.

Consider a car starts to move with an initial velocity (u) and its final velocity (v), which accelerates within the motion. The magnitude of the acceleration is (a) in the positive x-direction. Now to find out the time required to complete a motion, we use the first kinematical equation. The first kinematical equation of motion is,

Therefore,

u – Initial velocity of a car

v – Final velocity of a car

t – Time required to complete the motion

a – Acceleration of car

## When velocity and distance covered by object is given

When the question provides the magnitude of the velocity and the distance the object covers, we can quickly determine the time required for that motion. We know that velocity is the rate of change of displacement with respect to time. Mathematically written as,

Therefore,

By using the above formulae, we can calculate the time required to complete its motion.

**When velocity and acceleration are given**

When an object moves with continuously changing velocity, it means that the object is accelerating in motion with some magnitude (a). We know that acceleration is a rate of change of speed with respect to time. So if the question provides the magnitude of average velocity and acceleration of an object, we can easily find out the time required for that motion. As we know,

Therefore,

–

**Some Examples** and FAQ’s

**A bike starts to move with an initial speed of 30 m/sec and acceleration of 30 m/s**^{2} .After time t, its speed is 90 m/sec. How much time is a bike required to acquire its final speed?

^{2}.After time t, its speed is 90 m/sec. How much time is a bike required to acquire its final speed?

Given,

initial speed (u) – 30 m/s

Final speed (v) – 90 m/s

Acceleration – [latex]30m/s^{2}[/latex]

Here we have given an in initial velocity, final velocity, and also the acceleration of a bike then use a first kinematical equation to find out the time,

We know that the first kinematical equation of motion is

V = u + at

By putting the given values in the above equation

90 = 30 + 30t

Therefore,

t = 2 sec

Hence bike requires 2 sec to acquire the speed of 90 m/s.

**A car is moving at a speed of 50 m/s. How much time is it required to cover a 500 km distance?**

**Given, **speed of the car – 50 m/s

Covered distance – 500 km

To find – Required time to cover a distance

We know that velocity is a rate of change of distance with respect to time

i.e. Velocity = distance/time

Time = distance /velocity

t = 10000 sec

i.e. t = 2.7 hour

**A car moves from position A to position with a velocity of 30 m/s and acceleration of 3 m/** ** in a motion. How much time does it take to move from point A to point B?**

We know that acceleration is a change in velocity with respect to time.

Acceleration = velocity/ time

From the above equation, we can find the time required for a car to move from point A to B.

Time = velocity /acceleration

By putting the given values,

T = 30/3

Therefore, T = 10 sec

Hence car requires 10 sec to move from A to B

**FAQ’s**

**What is rectilinear motion of an object?**

** when an object performs motion in a straight line from point A to point B then that linear motion is called a rectilinear motion. **

**What is difference between speed and velocity?**

**Speed is a scalar quantity, while velocity is a vector quantity. Speed defines the magnitude with which an object is moving, and velocity gives magnitude and direction of objects motion. we can say that speed is a magnitude of the velocity.**

**What are the three kinematical equations of motion?**

**the three kinematical equations are as follows,**

**v =u + at****s = ut + 1/2 at**^{2}**v**^{2 }= u^{2}+ 2as

**where, s, a, t, u, v represents displacement, acceleration, initial velocity, final velocity and time of a motion respectively.**

**What is Average speed of an object?**

**average speed is a ratio of total distance traveled in a motion over the total time required to complete the motion. formulae of average speed is as follow,**