A driver is moving at 32 m/s when they see a deer in the road standing 74m in front of them. They hit the brake and slow down at a constant rate of 9.5m/s2. Will the driver hit the deer? this is a 2 part problem
To solve this two-part problem, we will first determine the time it takes for the driver to come to a stop and then calculate the distance the driver travels during that time.
Part 1: Calculating the time it takes to come to a stop
To find the time it takes for the driver to come to a stop, we can use the formula:
v = u + at
Where:
- v is the final velocity (0 m/s as the driver comes to a stop),
- u is the initial velocity (32 m/s),
- a is the acceleration (-9.5 m/s^2),
- t is the time taken.
Rearranging the formula to solve for time:
t = (v - u) / a
Substituting the given values:
t = (0 - 32) / -9.5
t = 3.37 seconds (rounded to two decimal places)
So, it takes approximately 3.37 seconds for the driver to come to a stop.
Part 2: Calculating the distance the driver travels during that time
To find the distance the driver travels during the 3.37 seconds it takes to stop, we can use the formula:
s = ut + (1/2)at^2
Where:
- s is the distance traveled,
- u is the initial velocity (32 m/s),
- t is the time taken (3.37 seconds),
- a is the acceleration (-9.5 m/s^2).
Substituting the given values:
s = 32(3.37) + (1/2)(-9.5)(3.37)^2
s = 53.76 - 56.5
s = -2.74 meters (rounded to two decimal places)
Since the distance traveled during the stopping time is negative (-2.74 meters), it means that the driver does not hit the deer. The negative sign indicates that the driver stops before reaching the deer, with a buffer distance of 2.74 meters.
Therefore, the driver does not hit the deer.