a car travelling at 50 km/h. the driver sees a child run out into the road 5 m ahead. she applies the breaks and the car stops in 5 second. the driver's thinking time is 1.5 s. a) will the car stop in time?
I need your help.
Pleace,help me by solving this problem.
To determine if the car will stop in time, we need to calculate the distance it will travel during the thinking time and the distance it will travel while decelerating.
First, let's find the distance the car will travel during the thinking time:
Thinking time = 1.5 seconds
Car's initial speed = 50 km/h
Thinking time distance = (initial speed) * (thinking time)
= (50 km/h) * (1.5 seconds)
To calculate this distance, we need to convert the initial speed from km/h to m/s first. We know that 1 km/h = (5/18) m/s.
Initial speed in m/s = (50 km/h) * (5/18)
= 13.89 m/s
Now we can calculate the thinking time distance:
Thinking time distance = (initial speed in m/s) * (thinking time)
= (13.89 m/s) * (1.5 seconds)
Next, let's find the distance the car will travel while decelerating. We know that the car decelerates uniformly and comes to a stop in 5 seconds.
Deceleration = (final speed - initial speed) / time
Final speed = 0 m/s (as the car comes to a stop)
Initial speed = 13.89 m/s (as calculated earlier)
Time = 5 seconds
Deceleration = (0 m/s - 13.89 m/s) / 5 seconds
Now, we can calculate the distance traveled while decelerating using the equation:
Distance = (initial speed) * (time) + (0.5) * (deceleration) * (time^2)
Distance while decelerating = (13.89 m/s) * (5 s) + (0.5) * (deceleration) * (5 s)^2
Finally, we can combine the thinking time distance and decelerating distance to find the total distance the car will travel:
Total distance = thinking time distance + distance while decelerating
Compare the total distance with the distance to the child, which is 5 meters. If the total distance is less than 5 meters, the car will stop in time. If it is greater than or equal to 5 meters, the car will not stop in time.