You are designing a simulation in which two characters moving along different paths are going to collide when the characters are at the same position at the same time. The position of the first character is given by y=2t , and the second is y=t+2 , y is in centimeters and t is the time in seconds. How many seconds after the simulation is started will the characters collide?(1 point)
Responses
3 seconds
3 seconds
4 seconds
4 seconds
1 second
1 second
2 seconds
2 seconds
To find the time when the characters collide, we need to find the point where the y-coordinates of both characters are equal.
For the first character, the position is given by y = 2t.
For the second character, the position is given by y = t + 2.
Setting these two expressions equal to each other, we have:
2t = t + 2
Simplifying the equation, we get:
t = 2
Therefore, the characters will collide 2 seconds after the simulation is started.
To find out when the characters will collide, we need to set their positions equal to each other and solve for the time (t) at which this occurs.
The position of the first character is given by y = 2t, and the position of the second character is given by y = t + 2.
Setting these two equations equal to each other:
2t = t + 2
Now, we can solve for t:
2t - t = 2
t = 2
Therefore, the characters will collide 2 seconds after the simulation is started. Hence, the correct answer is:
2 seconds