a truck travelling at a constant speed of 108 km/hr rounds a curve of radius 200m. calculate the acc of the truck

To find the acceleration of a truck traveling in a circular path, we need to consider the nature of circular motion. When an object moves in a circle, even at a constant speed, it is constantly changing its direction. This change in direction means there is an acceleration, known as centripetal acceleration, directed towards the center of the circle.

Centripetal Acceleration Formula

The formula to calculate centripetal acceleration (a) is:

a = v² / r

• v is the velocity of the truck.
• r is the radius of the curve.

Step 1: Convert Velocity to Meters per Second

The truck's speed is given as 108 km/hr. To use the formula, we need to convert this speed into meters per second (m/s). The conversion factor is:

1 km/hr = 1/3.6 m/s

Therefore:

v = 108 km/hr × (1/3.6 m/s) = 30 m/s

Step 2: Plugging Values into the Formula

Now that we have the speed in the correct units, we can substitute the values into the centripetal acceleration formula:

a = v² / r

a = (30 m/s)² / 200 m

a = 900 m²/s² / 200 m

a = 4.5 m/s²

Understanding the Result

The centripetal acceleration of the truck as it rounds the curve is 4.5 m/s². This means that even though the truck maintains a constant speed, it experiences an acceleration directed towards the center of the curve, allowing it to navigate the turn safely.

Real-World Application

This concept is crucial in various fields, including automotive engineering and road design. Understanding the forces at play when vehicles round curves helps in designing safer roads and vehicles that can handle such forces effectively.

Keep in mind that this acceleration is only the centripetal acceleration. If the truck were to speed up or slow down while rounding the curve, additional tangential acceleration would also need to be considered. However, since the problem states that the truck is traveling at a constant speed, we only focus on the centripetal acceleration in this scenario.