When braking, the car moves equally slowly along the highway with a rounding of the radius R

| February 21, 2021 | education

When braking, the car moves equally slowly along the highway with a rounding of the radius R and goes to a complete stop along the path S, having an initial speed V0. Determine the time of movement of the car to a complete stop and calculate the values of full accelerations at the initial moment and after time t1. R, = 100 S, = 70 V0 = 36 t1 = 4

Given: t = 0 s; V = 0 m / s; R = 100 m; S = 70 m; V0 = 36 km / h (10 m / s); t1 = 4 s.

1) Tangential acceleration: аτ = (V ^ 2 – V0 ^ 2) / 2S = (0 – 10 ^ 2) / (2 * 70) = -0.714 m / s2.

2) Time to full stop: t = (V – V0) / a = (0 – 10) / (- 0.714) = 14 s.

3) Full acceleration (t = 0 s): a = √ (an ^ 2 + aτ ^ 2) = √ ((V0 ^ 2 / R) ^ 2 + aτ ^ 2) = √ ((10 ^ 2/100) ^ 2 + 0.714 ^ 2) = 1.23 m / s2.

4) Full acceleration (t1 = 4 s): a = √ ((V1 ^ 2 / R) ^ 2 + aτ ^ 2) = √ (((V0 + aτ * t1) ^ 2 / R) ^ 2 + aτ ^ 2) = √ (((10 – 0.714 * 4) ^ 2/100) ^ 2 + 0.714 ^ 2) = 0.88 m / s2.



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