A object is throw up with a speed of 25m/s. suppose that the gravity is 10m/s^2. Define the position and the velocity of the particle for the following times: 1second, 4second and 10second
To define the position and velocity of a particle thrown up with a speed of 25m/s, we can use the equations of motion. Given that gravity is 10m/s^2 and assuming there is no air resistance, we can proceed as follows:
1. To find the position of the particle at a specific time, we use the equation of motion for displacement:
Displacement (s) = Initial velocity (u) * time (t) + (1/2) * acceleration (a) * time^2
At t = 1 second:
s = 25m/s * 1s + (1/2) * -10m/s^2 * (1s)^2
s = 25m - 5m
s = 20m
Therefore, the position of the particle at t = 1 second is 20 meters above the initial position.
At t = 4 seconds:
s = 25m/s * 4s + (1/2) * -10m/s^2 * (4s)^2
s = 100m - 80m
s = 20m
Therefore, the position of the particle at t = 4 seconds is also 20 meters above the initial position.
At t = 10 seconds:
s = 25m/s * 10s + (1/2) * -10m/s^2 * (10s)^2
s = 250m - 500m
s = -250m
Therefore, the position of the particle at t = 10 seconds is 250 meters below the initial position. The negative sign indicates the particle is now below the initial position.
2. To find the velocity of the particle at a specific time, we can use the equation of motion for velocity:
Velocity (v) = Initial velocity (u) + acceleration (a) * time (t)
At t = 1 second:
v = 25m/s + -10m/s^2 * 1s
v = 15m/s
Therefore, the velocity of the particle at t = 1 second is 15 m/s upwards (opposite to the direction of gravity).
At t = 4 seconds:
v = 25m/s + -10m/s^2 * 4s
v = -15m/s
Therefore, the velocity of the particle at t = 4 seconds is -15 m/s downwards.
At t = 10 seconds:
v = 25m/s + -10m/s^2 * 10s
v = -75m/s
Therefore, the velocity of the particle at t = 10 seconds is -75 m/s downwards.
Note: The negative velocities indicate that the particle is moving downwards opposite to the initial direction of motion (upwards).