Question

A motorist is traveling at 18.0 m/s when he sees a dog in the road 38.0 m ahead. (b) If his reaction time is actually 0.300 s, how fast will he be travelling when he hits the dog?

a) 18.0 m/s
b) 38.0 m
c) 0.300 s
d) 5.53 m/s

Answer 1

The final velocity of the motorist when he hits the dog is 5.53 m/s.

Step-by-step explanation:

To find the final velocity of the motorist when he hits the dog, we need to consider two factors: the distance traveled during the reaction time and the distance traveled without any reaction time

First, let's calculate the distance traveled during the reaction time:

1. Using the formula x = v0t + (1/2)at2, where x is the distance, v0 is the initial velocity, t is the time, and a is the acceleration, we can substitute the given values:
2. x = (18.0 m/s)(0.300 s) + (1/2)(0.0)(0.300 s)2 = 5.40 m

Next, let's calculate the distance traveled without any reaction time:

1. Using the formula x = v0t + (1/2)at2, we can substitute the given values:
2. x = (18.0 m/s)(0.000 s) + (1/2)(0.0)(0.000 s)2

The total distance traveled is the sum of these two distances: 5.40 m + 0.00 m = 5.40 m.

Therefore, the final velocity of the motorist when he hits the dog is 5.53 m/s.