A car is traveling around a horizontal circular track with radius r = 220 m at a

Question

A car is traveling around a horizontal circular track with radius r = 220 m at a constant speed v = 24 m/s as shown. The angle A = 25° above the x axis, and the angle B = 55° below the x axis.

The car's acceleration is 2.62m/s^2.

To find the x-component of the car's acceleration when it is at point A, I did a*cos, which is 2.62*cos(25)=2.37m/s^2. However, the answer is -2.37m/s^2. Why there is a negative sign?

Also, for the y-component when it's at point A, I did a*sin, which is 2.62*sin(25)=1.107m/s^2. But again the answer is -1.107m/s^2. I don't understand why both answers are negative. Please explain me why there is a negative sign?

Explanation / Answer

The car is experiencing centripetal acceleration at every point on the track, i.e., the acceleration is pointed towards the centre of the circle. The tangential acceleration is zero since the car is moving at constant speed. Centripetal acceleration provides change in direction without changing speed.

The acceleration vector is the line joining point A and centre of circle and the vector is directed towards centre of circle. Hence, this vector will have both negative x and y components.

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