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
Y(t) = 25 t - 5 t^2
V(t) = 25 - 10 t
Jyst plug in the different times t and compute the corresponding values of y (position) and V (velocity).
To define the position and velocity of the object at different times, we can use the equations of motion in physics. There are three equations of motion that relate the position (displacement), velocity, time, and acceleration. These equations are:
1. Displacement equation: d = v0t + (1/2)at^2
2. Velocity equation: v = v0 + at
3. Acceleration equation: v^2 = v0^2 + 2ad
In this case, we are given that the object is thrown upwards with an initial velocity of 25 m/s, and the acceleration due to gravity is -10 m/s^2 (negative sign denotes the direction). So, we will use a value of -10 m/s^2 for acceleration.
Let's calculate the position and velocity of the object at different times:
1. For t = 1 second:
Using the displacement equation, we have:
d = (25 m/s)(1 s) + (1/2)(-10 m/s^2)(1 s)^2
= 25 m - 5 m
= 20 meters (upwards)
Using the velocity equation, we have:
v = 25 m/s + (-10 m/s^2)(1 s)
= 25 m/s - 10 m/s
= 15 m/s (upwards)
So, at t = 1 second, the object's position is 20 meters upwards and its velocity is 15 m/s upwards.
2. For t = 4 seconds:
Using the displacement equation, we have:
d = (25 m/s)(4 s) + (1/2)(-10 m/s^2)(4 s)^2
= 100 m - 80 m
= 20 meters (downwards)
Using the velocity equation, we have:
v = 25 m/s + (-10 m/s^2)(4 s)
= 25 m/s - 40 m/s
= -15 m/s (downwards)
So, at t = 4 seconds, the object's position is 20 meters downwards and its velocity is -15 m/s downwards.
3. For t = 10 seconds:
Using the displacement equation, we have:
d = (25 m/s)(10 s) + (1/2)(-10 m/s^2)(10 s)^2
= 250 m - 500 m
= -250 meters (downwards)
Using the velocity equation, we have:
v = 25 m/s + (-10 m/s^2)(10 s)
= 25 m/s - 100 m/s
= -75 m/s (downwards)
So, at t = 10 seconds, the object's position is 250 meters downwards and its velocity is -75 m/s downwards.
Therefore, the position and velocity of the object for the given times are as follows:
- At t = 1 second: position = 20 meters upwards, velocity = 15 m/s upwards.
- At t = 4 seconds: position = 20 meters downwards, velocity = -15 m/s downwards.
- At t = 10 seconds: position = 250 meters downwards, velocity = -75 m/s downwards.