A delivery Is travelling at a constant speed of 15m/s in a 60 km.h speed zone when the driver seems people walking across a pedestrian crossing 50m ahead of him.the driver takes exactly one second to react before he applies brakes as hard as he can.it takes a further 3 seconds for the van to a stop.will the van stop before the pedestrian crossing?show all calculations.
In one second he moves 15m, leaving 35m for braking.
The speed decreases from 15m/s to 0 in 3 seconds, meaning the acceleration
a = -15/3 = -5 m/s^2
Now, the distance traveled will be
s(t) = 15t - 5/2 t^2
So, is s(3) less than 35m?
To determine if the van will stop before the pedestrian crossing, we need to calculate the distance it will travel during the reaction time and the distance it will take to stop.
First, we need to calculate the distance traveled during the driver's reaction time:
Distance = Speed x Time
The speed is given as 15 m/s, and the reaction time is given as 1 second.
Distance = 15 m/s x 1 s = 15 meters
So, during the driver's reaction time, the van will travel 15 meters.
Next, we need to calculate the distance it will take to stop:
To calculate the stopping distance, we can use the equation:
Stopping Distance = Initial Velocity x Stopping Time + (1/2) x Acceleration x (Stopping Time)^2
The initial velocity is 15 m/s and the stopping time is given as 3 seconds.
Acceleration during braking is negative as it opposes the motion, and it can be calculated using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
The final velocity is 0 m/s as the van comes to a stop.
Acceleration = (0 m/s - 15 m/s) / 3 s = -15 m/s / 3 s = -5 m/s^2
Now, we can substitute the values into the stopping distance equation:
Stopping Distance = 15 m/s x 3 s + (1/2) x (-5 m/s^2) x (3 s)^2
= 45 m - (1/2) x 5 m/s^2 x 9 s^2
= 45 m - 22.5 m
= 22.5 m
So, the van will take a distance of 22.5 meters to stop.
Now, sum up the distance traveled during the reaction time and the stopping distance:
Total Distance = Distance during Reaction Time + Stopping Distance
= 15 m + 22.5 m
= 37.5 meters
Therefore, the van will not stop before the pedestrian crossing as the total distance it will travel is 37.5 meters, which is greater than the 50-meter distance to the crossing.