Two particles move along the x-axis with uniform velocities of 8 m/s and 4 m/s. Initially, the first particle is 21 m to the left of the origin, and the second particle is 7 m to the right of the origin. The two particles meet at a distance of: 1) 35 m 2) 32 m 3) 28 m 4) 56 m
Answer (1)
To find the distance at which the two particles meet, we can use the concept of relative velocity and positions.
Let's define the positions and velocities:
Particle 1 :
Initial position: − 21 m (since it is to the left of the origin)
Velocity: 8 m/s
Particle 2 :
Initial position: 7 m (since it is to the right of the origin)
Velocity: 4 m/s
To find the time at which they meet, we set their positions equal:
The position of Particle 1 as a function of time t is: x 1 ( t ) = − 21 + 8 t
The position of Particle 2 as a function of time t is: x 2 ( t ) = 7 + 4 t
Setting these two positions equal: − 21 + 8 t = 7 + 4 t
Solving for t , 8 t − 4 t = 7 + 21 4 t = 28 t = 4 28 t = 7 seconds
Now, we can find the position at which they meet using either particle's position function. Using Particle 1's position function: x 1 ( 7 ) = − 21 + 8 × 7 x 1 ( 7 ) = − 21 + 56 x 1 ( 7 ) = 35
The two particles meet at a distance of 35 meters from the origin. Therefore, the correct answer is:
35 m
