A driver enters a curve with 150 m radius at a speed of 20 m/s and begins brakin

Question

A driver enters a curve with 150 m radius at a speed of 20 m/s and begins braking. As he applies his brakes he decreases his speed at a constant rate of 1.5 m/s^2. Calculate the magnitude of the total acceleration of the car when its speed is 18 m/s.

A driver enters a curve with 150 m radius at a speed of 20 m/s and begins braking. As he applies his brakes he decreases his speed at a constant rate of 1.5 m/s2. Calculate the magnitude of the total acceleration of the car when its speed is 18 m/s.

Explanation / Answer

given that

r = 150 m

v = 20 m/s

a = 1.5 m/s^2

tangential acceleration = at = 1.5 m/s^2

centripetal acceleration = ac = v^2/r = 18*18 / 150 =

magnitude of total acceleration a total = sqrt(at2 + ac2) = sqrt( (1.5)2 + (2.16)2) = 2.62 m/s^2

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