Understanding Uniform Acceleration: Calculating Distance and Velocity

The concept of uniform acceleration is fundamental in mechanics and physics, particularly in the study of motion. Uniform acceleration is defined as a constant rate of change of velocity. In this article, we will explore how to calculate the acceleration and distance traveled by a car that accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. This process will be explained using the SUVAT equations, a cornerstone of kinematics.

The SUVAT Equations and Uniform Acceleration

The SUVAT equations, named after the variables they utilize (Speed, Uniform, Time, Acceleration, and Distance), are a set of five equations that describe the motion of a particle moving in a straight line with uniform acceleration. The equations are as follows:

s ut 0.5at^2 - where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration. v u at - where v is the final velocity. s 0.5(v u)t - an alternate form of the distance equation. v^2 u^2 2as - for solving for acceleration and distance. v u at - again, to find final velocity.

These equations provide a systematic approach to solving problems involving uniform acceleration.

Calculating the Car's Acceleration

Given the scenario where a car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds, let's first calculate the acceleration. Using the kinematic equation:

Equation 1: a (v - u) / t

where:

u 0 m/s (initial velocity, as the car starts from rest) v 20 m/s (final velocity) t 10 s (time taken to reach the final velocity)

Plugging in the values:

a (20 m/s - 0 m/s) / 10 s 2 m/s^2

The car's acceleration is 2 m/s^2.

Calculating the Distance Traveled

Now, let's calculate the distance traveled during this time. We can use the kinematic equation:

s ut 0.5at^2

Substituting the known values:

u 0 m/s t 10 s a 2 m/s^2

Thus:

s 0 × 10 s 0.5 × 2 m/s^2 × 10 s^2 0 100 m 100 m

The car travels 100 meters in 10 seconds.

Using Alternative Equations

For a more general approach, let's use the alternative form of the SUVAT equation:

s (v^2 - u^2) / (2a)

Substituting the known values:

u 0 m/s v 20 m/s a 2 m/s^2

Thus:

s (20^2 - 0^2) / (2 × 2) 400 / 4 100 m

This confirms that the car travels 100 meters during the acceleration period.

Conclusion

In summary, the car's acceleration is 2 m/s^2 and the distance it travels in 10 seconds is 100 meters. The SUVAT equations offer a powerful and systematic way to solve problems involving uniform acceleration and motion in a straight line. Understanding these equations and their application is essential for anyone studying physics, engineering, or related fields.