Question

A car traveling 54.3 km/h is 24.3 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.14 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact?

Answer 1

Question #51365, Physics, Mechanics | Kinematics | Dynamics

A car traveling 54.3 km/h is 24.3 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.14 s later. (a) What is the car's constant deceleration magnitude before impact? (b) How fast is the car traveling at impact?

Answer.

$$S = V _ {0} t - \frac {a t ^ {2}}{2}, \ V = V _ {0} - a t.$$

In our case:

$$S = 24.3 \ m, \ V _ {0} = 54.3 \ \frac {k m}{h} = 54.3 \ * \frac {1000}{60 \ * 60} = 15.08 \ \frac {m}{s}, \ \ \ \ t = 2.14 \ s.$$

(a) $a = \frac{2(Vt - S)}{t^2} = \frac{2(15.08 * 2.14 - 24.3)}{2.14^2} = 3.48 \ \frac{m}{s^2}$

(b) $V = 15.08 - 3.48 * 2.14 = 7.63 \ \frac{m}{s}$

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