a driver of a car going 95.0km/h suddenly sees the lights of a barrier 35.0 m aheadd. It takes the driver 95 s before he applies the breaks, and the average acceleraion during breaking is -10.om/s/s does the car hit the barrier?
To determine if the car hits the barrier, we need to analyze the motion of the car and calculate the distance it travels before it comes to a stop.
Given data:
Initial velocity (u) = 95.0 km/h = 95.0 × (1000 m/1 km) / (3600 s/1 h) = 26.39 m/s
Distance to the barrier (s) = 35.0 m
Time taken to apply the brakes (t) = 95 s
Acceleration during braking (a) = -10.0 m/s² (negative because it is deceleration)
To find out if the car hits the barrier, we need to calculate the distance it will travel during the 95 second time span.
Using the equation of motion: s = ut + (1/2)at²
Substituting the given values:
s = (26.39 m/s) * (95 s) + (1/2) * (-10.0 m/s²) * (95 s)²
Calculating the distance traveled:
s = 2500 m
The car will travel a distance of 2500 meters during the 95 second time span. Since this distance is greater than the distance to the barrier (35.0 m), we can conclude that the car will hit the barrier.