If the car\'s speed is increasing at a known rate as it travels along a curve, h

Question

If the car's speed is increasing at a known rate as it travels along a curve, how can we determine the magnitude and direction of its total acceleration? Why would you care about the total acceleration of the car?

1. Cars traveling along a clover-leaf interchange experience an acceleration due to a change in velocity as well as due to a change in direction of the velocity. If the car's speed is increasing at a known rate as it travels along a curve, how can we determine the magnitude and direction of its total acceleration? Why would you care about the total acceleration of the car

Explanation / Answer

As car is travel along a curve so it must have two acceleration:

1. Centripetal acceleration acting along the center of the at that point of the curvature where we want to know the acceleration on it. And centripetal acceleration is given by the equation ac=v^2/r , v is Velocity at point and r is radius of curvature of that instant.

2.Second is the tengential acceleration which is because of change in the magnitude of the velocity in the circular path.and it is given by at= dv/dt.

Both these are perpendicular to each other.so one should have to add them vectorically for total acceleration.

Hope it will help!

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