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A car is traveling at a constant speed of 30 m/s along a straight road. The driver suddenly applies the brakes, causing the car to decelerate at a rate of 5 m/s^2. Calculate the time it takes for the car to come to a complete stop and the distance it travels during this time. Solution: To solve this problem, we can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.

answer

Initial velocity, u = 30 m/s Acceleration, a = -5 m/s^2 (negative because it is deceleration) Final velocity, v = 0 m/s (since the car comes to a complete stop) Using the equation of motion, we can rearrange it to solve for distance, s: s = (v^2 - u^2) / (2a) Substituting the given values: s = (0^2 - 30^2) / (2 * -5) s = (-900) / (-10) s = 90 meters Now, to find the time taken, we can use the equation of motion: v = u + at Rearranging the equation to solve for time, t: t = (v - u) / a Substituting the given values: t = (0 - 30) / -5 t = 30 / 5 t = 6 seconds Therefore, it takes 6 seconds for the car to come to a complete stop, and it travels a distance of 90 meters during this time.

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