Calculating Acceleration Using Given Data in Physics Problems

Understanding the concept of acceleration and how to apply it in a given scenario is a fundamental part of physics. In this article, we will discuss a specific problem related to acceleration and demonstrate multiple methods to solve it. We'll also provide a step-by-step solution using the SUVAT equations, which are critical in solving problems involving motion.

Problem Statement:

A body starts from rest and covers 120 meters in the 8th second. What is the acceleration of the body?

Understanding the Basics of Acceleration

First, let's understand the concept of acceleration. Acceleration is the rate at which an object's velocity changes over time. In mathematical terms, it is the first derivative of velocity with respect to time. The unit of acceleration is meters per second squared (m/s2).

Solving the Problem

The problem involves determining the acceleration of a body that starts from rest and covers 120 meters in the 8th second. This requires a bit of insight into the physics behind the scenario.

METHODS TO SOLVE THE PROBLEM

Method 1: Direct SUVAT Equation Application

We can use the SUVAT equations (for motion under constant acceleration) to solve this problem. The specific equation we need is one that relates distance covered to acceleration, initial velocity, and time:

S ut 0.5at2

Where:

S is the distance covered,u is the initial velocity,a is the acceleration,t is the time.

The body starts from rest, so the initial velocity, u, is zero. The distance covered in the 8th second is 120 meters, and the time is from t 7 to t 8 seconds.

The distance covered in the 8th second can be calculated using the SUVAT equation for the total distance covered up to t 8 seconds and subtracting the distance covered up to t 7 seconds.

Equation 1: S8 0.5a(82)

Equation 2: S7 0.5a(72)

The distance covered in the 8th second is:

120 0.5a(82) - 0.5a(72)

120 0.5a(64 - 49)

120 0.5a(15)

120 7.5a

a 16 m/s2

Method 2: Simplified Acceleration Calculation

A simpler approach would be to directly consider the distance covered in one second:

The distance covered in the 8th second is given as 120 meters. This distance can be directly related to the acceleration using the formula for distance covered in a specific time under uniform acceleration:

S ut 0.5at2

Since the initial velocity is zero (u 0), the equation simplifies to:

S 0 0.5a(82 - 72)

120 0.5a(64 - 49)

120 0.5a(15)

120 7.5a

a 16 m/s2

Method 3: First Principles and Equations of Motion

Using first principles and the equations of motion, we can also derive the acceleration:

x ut 0.5at2

At t 8 seconds, the total distance covered is 120 meters. We need to find the acceleration:

120 0 0.5a(82 - 72)

120 0.5a(64 - 49)

120 0.5a(15)

120 7.5a

a 16 m/s2

Understanding SUVAT Equations

The SUVAT equations are:

x ut 0.5at2v u at2as v2 - u2x2 - x1 ut2 - ut1 0.5a(t22 - t12)

These equations are used to solve problems involving motion under constant acceleration.

Conclusion

By using the SUVAT equations and understanding the concept of acceleration, we can easily solve problems related to motion under constant acceleration. In this article, we demonstrated multiple methods to solve the problem of determining the acceleration of a body that covers 120 meters in the 8th second. The final answer is 16 m/s2.

Resources and Recommended Readings

For a deeper understanding of physics and motion under constant acceleration, consider reading the following resources:

Textbook: Physics for Scientists and Engineers by Raymond A. Serway and John W. JewettOnline Courses: Coursera’s Motion, Force, and Energy by University of Colorado BoulderYouTube Channels: Physics Gal and Let’s Talk Physics