Question

The Truck is moving with velocity of 60 m/sec, suddenly brake applied on it. If time taken is 5 second
find distance covered after application of brake?​

Answer 1

These equations are for a particle moving in a straight line with a constant acceleration.

The history of these equations is not absolutely clear, but we do have some knowledge.

In the 14th century, scholastic philosophers at Merton College, Oxford, studied motion

with constant acceleration and deduced what is now known as the Merton rule:

An object with constant acceleration travels the same distance as it would

have if it had constant velocity equal to the average of its initial and final

velocities.

In the 17th century, Galileo Galilei (1564–1642) and others discovered that, in a void, all

falling objects have the same constant acceleration. Newton (1642–1727) and Leibniz

(1646–1716) built on these ideas in developing the concept of the derivative.

In the following:

• u is the initial velocity of the particle

• v is the final velocity of the particle

• a is the constant acceleration of the particle

• t is the time of motion

• x is the distance travelled.

The equations are as follows:

1 v = u + at

2 x = ut +

1

2

at 2

3 x =

(u + v)t

2

4 v

2 = u

2 +2ax

5 x = v t −

1

2

at 2

.

Note. Each of the five equations involve four of the five variables u, v,a,t,x. If the values

of three of the variables are known, then the remaining values can be found by using two

of the equations.

We can use calculus to help derive these five equations.