Answer :
Final answer:
By applying equations of motion, we can solve for time, considering the car's initial speed and the distance covered during braking. The final velocity is zero, and using this we find the acceleration. Adding acceleration to the original equation of motion allows us to solve for time, when the car stops.
Explanation:
To solve this problem, we use the equation of motion that relates displacement, initial velocity, and acceleration: x = ut + 1/2at², where x is displacement, u is initial velocity, t is time, and a is acceleration. We know the car comes to stop, so its final velocity is zero. Considering the car's motion from start to stop, we have an equation that relates initial and final velocities, acceleration, and time: v = u + at. Here, v is final velocity, which is 0m/s. Substitute these values into the equation: 0 = 12.8 m/s + a*t. We can rearrange this equation to find acceleration: a = -12.8m/s / t.
Substituting this expression for a into the original equation of motion, we get: 34.3 m = 12.8 m/s * t + 1/2 * (-12.8 m/s / t) * t². Simplifying this equation, we can solve for t, which gives the time it took for the car to stop.
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