A motorist with an expired license tag travels at a constant speed of 17.2 m/s down a street, and a policeman on a motorcycle, taking another 4.08 s to finish his donut, gives chase at an acceleration of 2.71 m/s2.
x is distance from donut shop
t is time police chases, so car is 4.08 seconds more
when they are both x meters from shop:
x = 17.2 ( t+4.08)
x = (1/2) 2.71 t^2
when they meet
1.35 t^2 = 17.2 t + 70.2
or
1.35 t^2 -17.2 t - 70.2 = 0 solve quadratic
https://www.mathsisfun.com/quadratic-equation-solver.html
so t = -1.78 or t = 3.16
negative time was before the car started so use 3.16 seconds
then the car went 3.16 + 4.08 = 7.24 seconds
and they meet 17.2 * 7.24 = 125 meters from donuts
d1 = d2.
17.2*4.08 + 17.2*T = 0.5*a*T^2.
70.2 + 17.2T = 0.5*2.71*T^2,
1.35T^2 - 17.2T - 70,2 = 0,
T^2 - 12.7T - 52 = 0, Use Quad. Formula.
T = (12.7 +- sqrt(162 + 208))/2 = (12.7 +- 370)/2 = 16, and -3.3 s.
T = 16 s.
d = 0.5*2.71*16^2 = 347 m.
To find the time it takes for the policeman to catch up with the motorist, we need to first find the distance traveled by both the motorist and the policeman.
1. Distance traveled by the motorist:
The motorist travels at a constant speed of 17.2 m/s. Since we have no information about how long the motorist has been driving, we need an additional piece of information to calculate the distance traveled.
2. Distance traveled by the policeman:
The policeman starts from rest and accelerates at 2.71 m/s². The time it takes him to finish his donut is given as 4.08 s.
To find the distance traveled by the policeman, we can use the equation:
distance = initial velocity * time + (0.5 * acceleration * time²)
Here, initial velocity = 0 m/s (as the policeman starts from rest), time = 4.08 s, and acceleration = 2.71 m/s².
Substituting the values into the equation, we get:
distance = 0 * 4.08 + (0.5 * 2.71 * (4.08)²)
= 0 + (0.5 * 2.71 * 16.6464)
= 0 + 22.767104
= 22.767104 m
3. Now, we need to find the time it takes for the policeman to catch up with the motorist.
Let's assume this time to be 't'.
The motorist will travel this time 't' at a constant speed of 17.2 m/s.
Since the policeman is accelerating uniformly, we can use the equation:
distance = initial velocity * time + (0.5 * acceleration * time²)
Here, initial velocity = 0 m/s (as the policeman starts from rest), acceleration = 2.71 m/s², and distance = 22.767104 m.
Substituting the values into the equation, we get:
22.767104 = 0 * t + (0.5 * 2.71 * t²)
22.767104 = 1.3555 * t²
t² = 16.799618635
t ≈ √16.799618635
t ≈ 4.10 s
Therefore, it will take approximately 4.10 seconds for the policeman to catch up with the motorist.
To answer this question, we need to determine the time it takes for the policeman to catch up with the motorist. We can do this by using the equations of motion.
Let's break down the problem step by step:
1. Determine the initial distance between the motorist and policeman.
To do this, we need to know how long the motorist has been traveling before the chase begins. If we have that information, we can calculate the initial distance traveled by the motorist using the formula:
Initial distance = (Initial speed) x (Time before chase begins)
2. Find the time it takes for the policeman to catch up with the motorist.
The equation we will use for this step is:
Distance = (Initial speed x Time) + (0.5 x Acceleration x Time^2)
In this case, the distance will be the initial distance calculated in step 1. We will solve this equation for the time it takes for the policeman to catch up.
Let's plug in the values given in the question:
Initial speed of the motorist = 17.2 m/s
Acceleration of the policeman = 2.71 m/s^2
Time required for the policeman to finish his donut = 4.08 s
Now, let's solve the problem:
1. Determine the initial distance between the motorist and policeman:
Initial distance = (17.2 m/s) x (Time before chase begins)
Since we don't have the information about the time before the chase begins, we won't be able to determine the initial distance accurately. Hence, we can't proceed to step 2 without that information.
Note: It's important to have all the necessary information to accurately solve a problem. In this case, we are missing the time before the chase begins.