A test car starts from rest on a horizontal circular track of 80-m radius and increases its spee

step 1 Starting from rest, so u equals to 0 and reaching v equals to 100 km per hour in time t equals t

A test car starts from rest on a horizontal circular track...

A test car starts from rest on a horizontal circular track of $80-\mathrm{m}$ radius and increases its speed at a uniform rate to reach $100 \mathrm{km} / \mathrm{h}$ in 10 seconds. Determine the magnitude $a$ of the total acceleration of the car 8 seconds after the start.

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Key Concepts

Uniform Tangential Acceleration

This concept refers to the change in the magnitude of the velocity of an object moving along a path, calculated as the change in speed over time. It is particularly important in scenarios where an object speeds up or slows down while moving along a curved path, and it represents the acceleration component that acts along the direction of motion.

Centripetal (Radial) Acceleration

This acceleration component is always directed towards the center of a circular path and is responsible for changing the direction of the velocity vector of an object moving in a circle. It is given by the formula v²/r, where v is the speed of the object and r is the radius of the circle. It is crucial for maintaining circular motion.

Vector Addition of Acceleration Components

In situations where an object experiences both tangential and centripetal accelerations, the overall acceleration is determined by the vector sum of these perpendicular components. Since they act in mutually perpendicular directions, the total acceleration magnitude can be obtained by applying the Pythagorean theorem to the individual acceleration components.

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