A car is traveling 17 m/s when the driver sees a child standing on the road. He takes 0.8 s to react, then steps on the brakes and slows at 7.0 m/s2. How far does the car go before it stops?

To find the distance the car travels before it stops, we can use the equation of motion for uniformly decelerated motion:

š‘‘ = š‘£ā‚š‘” + 1/2š‘Žš‘”Ā²

Where:
š‘‘ is the distance traveled
š‘£ā‚ is the initial velocity
š‘” is the time taken to stop
š‘Ž is the acceleration

Given:
š‘£ā‚ = 17 m/s (initial velocity)
š‘” = 0.8 s (time taken to react)
š‘Ž = -7.0 m/sĀ² (acceleration)

First, we need to find the distance traveled during the reaction time. We do this by multiplying the initial velocity by the reaction time:

š‘‘ā‚ = š‘£ā‚ Ɨ š‘”

š‘‘ā‚ = 17 m/s Ɨ 0.8 s = 13.6 m

Now, we can find the distance traveled during the deceleration phase:

š‘‘ā‚‚ = 1/2 Ɨ š‘Ž Ɨ š‘”Ā²

š‘‘ā‚‚ = 1/2 Ɨ -7.0 m/sĀ² Ɨ (š‘” + š‘”)

š‘‘ā‚‚ = -7.0 m/sĀ² Ɨ 1.6 s

š‘‘ā‚‚ = -11.2 m

Note: The negative sign indicates that the car is decelerating.

Finally, add the distances traveled during the reaction time and the deceleration phase to find the total distance traveled before the car stops:

š‘‘ = š‘‘ā‚ + š‘‘ā‚‚

š‘‘ = 13.6 m + (-11.2 m)

š‘‘ = 2.4 m

Therefore, the car travels 2.4 meters before it stops.