Kinematics and Accelerated Motion: Calculating Distance Covered by a Body

Understanding the motion of objects is a fundamental concept in physics. In this article, we will explore the calculation of the distance covered by a body undergoing uniform acceleration. We will use a given example to illustrate the mathematical principles involved.

What is Accelerated Motion?

Accelerated motion refers to the change in velocity of an object over time. In such cases, the body's velocity increases or decreases at a constant rate, known as acceleration. The units for velocity are meters per second (m/s), while the units for acceleration are meters per second squared (m/s2).

Example Problem

Consider a scenario where a body moves with an initial velocity of 30 m/s and accelerates uniformly at a rate of 10 m/s2 until it attains a final velocity of 50 m/s. We aim to calculate the distance covered during this period.

Using Kinematic Equations

To solve this problem, we will utilize one of the four kinematic equations. Specifically, we will use the equation:

v2 u2 2as

Where:

v final velocity (50 m/s) u initial velocity (30 m/s) a acceleration (10 m/s2) s distance to be determined (in meters)

Lets solve for s by rearranging the equation:

s (v2 - u2) / (2a)

Substituting the given values:

s (502 - 302) / (2 * 10)

Calculating the values:

s (2500 - 900) / 20

s 1600 / 20

s 80 m

Therefore, the distance covered during the period of acceleration is 80 meters.

Deriving the Distance from Velocity-Time Graph

We can also derive the distance covered by considering the relationship between velocity, acceleration, and time. The equation for the distance covered during uniform acceleration can be expressed as:

s v?t (1/2)at2

Where:

s distance covered v? initial velocity a acceleration t time

The final velocity after a certain time can be expressed as:

v v? at

Solving for the time t when the final velocity v is 50 m/s:

t (50 - 30) / 10

t 2 s

Using the distance formula:

s 30 * 2 (1/2) * 10 * 22

s 60 (10/2) * 4

s 60 20

s 80 m

Again, the distance covered is 80 meters.

Conclusion

Through both the kinematic equations and the velocity-time relationship, we have demonstrated the method to calculate the distance covered by an accelerating body. Understanding and applying kinematic equations is crucial for analyzing motion and solving physics problems.

Related Keywords

Physics Accelerated Motion Kinematics Equations Distance Calculation