A young woman named Kathy Kool buys a sports car that can accelerate at the rate of 4.6 m/s2. She decides to test the car by dragging with another speedster, Stan Speedy. Both start from rest, but experienced Stan leaves the starting line 0.8 s before Kathy. If Stan moves with a constant acceleration of 3.6 m/s2 and Kathy maintains an acceleration of 4.6 m/s2
a) Find the time it takes Kathy to overtake Stan.
b) Calculate the distance she travels before she catches him.
c) Calculate the speed of Kathy's car at the instant she overtakes Stan.
d) Calculate the speed of Stan's car at the instant he is overtaken by Kathy.
I've looked at questions worded the same with different numbers but I just can't get it.
When Kathy overtakes Stan they covered
the same distances s1=s2
s1 =a1•t^2/2
s2=a2•(t+0.8)^2/2
a1•t^2/2 = a2•(t+0.8)^2/2
t = 1.93s
s1 = 4.6•(1.93)^2/2 =8.58 m
V1 = a1•t =4.6•1.93 = 8.878 m/s
V2 = a2•(t+0.8) = 3.6•2.73 = 6.33 m/s
To solve this problem, we need to apply kinematic equations of motion. These equations describe the relationships between distance, time, velocity, and acceleration.
Let's start by identifying the given information:
Kathy's acceleration (Kathy's car): a1 = 4.6 m/s^2
Stan's acceleration (Stan's car): a2 = 3.6 m/s^2
Time difference (delay): t = 0.8 s
Now, let's solve the problem step by step:
a) Find the time it takes Kathy to overtake Stan:
To find the time it takes for Kathy to catch up with Stan, we need to calculate the time it takes for both cars to cover the same distance. We'll refer to this time as t_catch.
The equation to calculate the displacement (distance) covered by an object with constant acceleration is:
s = ut + (1/2)at^2
For Kathy's car:
s1 = u1t_catch + (1/2)a1t_catch^2
For Stan's car:
s2 = u2(t_catch + t) + (1/2)a2(t_catch + t)^2
In both equations, u stands for the initial velocity, which is zero in this case because both cars start from rest.
Since we want to find the time Kathy overtakes Stan, we need to set the displacements s1 and s2 equal to each other:
u1t_catch + (1/2)a1t_catch^2 = u2(t_catch + t) + (1/2)a2(t_catch + t)^2
Now, we can solve this equation for t_catch.
b) Calculate the distance Kathy travels before she catches Stan:
To find the distance Kathy travels before she catches Stan, we need to substitute the value of t_catch into one of the equations for displacement.
We can use Kathy's equation:
s1 = u1t_catch + (1/2)a1t_catch^2
c) Calculate the speed of Kathy's car at the instant she overtakes Stan:
To find the speed of Kathy's car at the moment she overtakes Stan, we can use the equation for velocity:
v = u + at
Plug in the values for u1 and a1 into this equation, and use the value of t_catch.
d) Calculate the speed of Stan's car at the instant he is overtaken by Kathy:
To find the speed of Stan's car at the moment he is overtaken by Kathy, we can also use the equation for velocity:
v = u + at
Plug in the values for u2 and a2 into this equation, and use the value of t_catch.
Now that we have formulated the problem and identified the relevant equations, you can use these equations to calculate the values for each part of the problem.