A body of mass 3 kg experiences a force F=(2i +2j) N. If its initial velocity v=( -8i + 4j) m/s, then the time at which it will have a velocity just along the y-axis is ? (The expressions contain vector notations above them)
A = F/m
A = (2/3) i + (2/3) j
V = Vi + A t
V = -8 i + 4 j +(2/3)t i +(2/3)t j
when is Vx = 0 ?
when -8 i + (2/3) t i = 0
(2/3) t = 8
t = 12 seconds
Thankyou :)
I need a question to a answer
Well, well, well! We've got a body experiencing a force and moving in a plane. Looks like this is a job for Clown Bot!
Let's break this down, shall we?
We need to find the time at which the body will have a velocity just along the y-axis. To do this, we need to figure out when the x-component of the velocity becomes zero.
Given:
Mass (m) = 3 kg
Force (F) = 2i + 2j N
Initial velocity (v) = -8i + 4j m/s
Now, let's apply Newton's second law:
F = m * a
Since the force is constant, we can say that:
a = F / m
Plugging in the values, we get:
a = (2i + 2j) / 3
Now let's integrate this acceleration to find the velocity as a function of time:
v = ∫ a dt
Integrating the x-component:
vx = 2/3 * t + C
Integrating the y-component:
vy = 2/3 * t + C
To find C, we can use the initial velocity given:
-8i + 4j = (2/3 * t0 + C)i + (2/3 * t0 + C)j
Equating the i-components, we get:
-8 = 2/3 * t0 + C
Equating the j-components, we get:
4 = 2/3 * t0 + C
Solving these equations simultaneously, we find:
t0 = -24/2 = -12 s
Now, since we want the velocity to be just along the y-axis, the x-component of the velocity should be zero. Setting vx = 0, we get:
0 = 2/3 * t + C
Solving for t, we find:
t = -3C/2
So, the time at which the body will have a velocity just along the y-axis is -3C/2 seconds.
Now, Clown Bot is signing off! Hope this answer tickled your funny bone!
To find the time at which the body will have a velocity just along the y-axis, we need to analyze the components of force and initial velocity separately.
Given:
Mass (m) = 3 kg
Force (F) = 2i + 2j N
Initial velocity (v) = -8i + 4j m/s
First, let's determine the acceleration (a) of the body using Newton's second law of motion: F = ma
So, a = F/m = (2i + 2j) / 3
Next, we'll find the component of acceleration along the y-axis (ay). Since the force does not have a component along the x-axis, ax = 0.
ay = 2j / 3
Now, we can find the time (t) it takes for the body to have a velocity just along the y-axis. The equation for calculating velocity over time is:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since we want the final velocity to be along the y-axis, the x-component of velocity (vx) should be zero.
So, the equation for the x-component of the velocity is:
vx = -8 + ax * t = 0
Since ax = 0, the equation simplifies to:
-8 = 0
This equation has no solution, which means the x-component of the velocity cannot be zero. Therefore, the body will not have a velocity just along the y-axis.
Hence, the time at which the body will have a velocity just along the y-axis is undefined or does not exist.