A motorist suddenly notices a stalled car and slams on the brakes, decelerating

Question

A motorist suddenly notices a stalled car and slams on the brakes, decelerating at the rate of 6.3 . Unfortunately this isn't good enough, and a collision ensues. From the damage sustained, police estimate that the car was moving at 18 at the time of the collision. They also measure skid marks 34 long. How fast was the motorist going when the brakes were first applied? How much time elapsed from the initial braking to the collision? use two sig figs

Explanation / Answer

A motorist suddenly notices a stalled car and slams on the brakes, decelerating at the rate of 6.3 m/s^2.? Unfortunately this isn't good enough, and a collision ensues. From the damage sustained, police estimate that the car was moving at 18 km/h at the time of the collision. They also measure skid marks 34 m long. Part A. How fast was the motorist going when the brakes were first applied? Part B. How much time elapsed from the initial braking to the collision? 18 km/h = 18000/3600 m/s = 5 m/s V^2 - 5^2= 2*6.3*34 or V^2 = 25 + 428.4 = 21.29 m/s or 21.3 m/s or 76.65 or 77 km/h Time elapsed = (21.3 -5)/6.3 = 2.58 or 2.6 s A motorist suddenly notices a stalled car and slams on the brakes, decelerating at the rate of 6.3 m/s2. Unfortunately this isn't good enough, and a collision ensues. From the damage sustained, police estimate that the car was moving at 20 km/h at the time of the collision. They also measure skid marks 29 m long. (a) How fast was the motorist going when the brakes were first applied? (b) How much time elapsed from the initial braking to the collision? a) The initial speed of the car was : v² = v0² + 2a?x Solve for initial velocity, v0: v0² = v² - 2a?x = (5.6m/s)² - 2(-6.3m/s²)(29m)--->20km/h = 5.6m/s = 19m/s (b) Now, the time from braking to collision is : v = v0 + at t = (v - v0) / a = (5.6m/s - 19m/s) / -6.3m/s²) = 2.1s A motorist suddenly notices a stalled car and slams on the brakes, decelerating at a rate of 6.3m/s^2. Unfortunately, this isn't good enough, and a collision ensues. From the damage sustained, police estimate that the car was moving at 18km/h at the time of the collision. They also measure skid marks 34m long. How fast was the motorist going when the brakes were first applied? Answer Assuming uniform deceleration... V2 = Vo2 + 2a(X – Xo) a = Acceleration V = Velocity Vo = Initial Velocity X = Displacement Xo = Initial Position 18 km/h = 5 m/s (5 m/s)2 = Vo2 + 2(-6.3 m/s2)(34 m - 0) Vo = 21.3 m/s = 76.7 km/h

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