The speed of a car increases uniformly with time from 50 km / h at A to 100 km / h at B during 1

step 1 Total acceleration is same for both conditions A and B. So we can write that a tangential A squa

The speed of a car increases uniformly with time from 50 km...

The speed of a car increases uniformly with time from $50 \mathrm{km} / \mathrm{h}$ at $A$ to $100 \mathrm{km} / \mathrm{h}$ at $B$ during $10 \mathrm{sec}$ onds. The radius of curvature of the hump at $A$ is $40 \mathrm{m} .$ If the magnitude of the total acceleration of the mass center of the car is the same at $B$ as at $A,$ compute the radius of curvature $\rho_{B}$ of the dip in the road at $B$. The mass center of the car is $0.6 \mathrm{m}$ from the road.

The speed of a car increases uniformly with time from $50 \mathrm{km} / \mathrm{h}$ at $A$ to $100 \mathrm{km} / \mathrm{h}$ at $B$ during $10 \mathrm{sec}$ onds. The radius of curvature of the hump at $A$ is $40 \mathrm{m} .$ If the magnitude of the total acceleration of the mass center of the car is the same at $B$ as at
$A,$ compute the radius of curvature $\rho_{B}$ of the dip in the road at $B$. The mass center of the car is $0.6 \mathrm{m}$ from the road.

Key Concepts

Resultant Acceleration

Resultant acceleration is the vector sum of the tangential and centripetal acceleration components. It represents the total acceleration experienced by an object moving along a curved path and is computed using the Pythagorean theorem when the two components are perpendicular.

Radius of Curvature

The radius of curvature quantifies the sharpness of the curve along which the object is moving. In circular motion, it is directly related to the centripetal acceleration, with a smaller radius producing a higher centripetal acceleration for a given speed.

Uniform Acceleration

This concept relates to the change in the speed of an object at a constant rate over time. It is crucial in kinematics as it allows one to determine the tangential acceleration, which is the rate of increase of the object's speed along its path.

Tangential Acceleration

Tangential acceleration is the component of an object's acceleration that is directed along the tangent to the path. It represents the rate at which the speed of the object is changing and is obtained from the uniform change in speed over time.

Centripetal Acceleration

Centripetal acceleration is directed towards the center of curvature of the path and accounts for the change in the direction of the velocity vector during motion along a curved path. It is determined by the square of the speed divided by the radius of curvature.

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