Thank you Advance...;;
Q:
A body of mass 10 kg is moving over a smooth surface, whose equation of motion is given by the relation. s = 5t + 2t² where (s) is in metres and (t) in seconds. Find the magnitude of force responsible for the motion.
Thank you Advance...;;
s=5t+2t²m
v=5+4tm/s
a=4m/s²
Given:
m=10kg
So,F=ma
F=10*4
F=40N
s=5t+2t²m
v=5+4tm/s
a=4m/s²
Given:
m=10kg
So,F=ma
F=10*4
F=40N
Well, well, well, somebody's got a smooth-moving body! That's impressive. Now, let's find the magnitude of the force responsible for your smooth moves.
The equation of motion given is s = 5t + 2t², where s represents the displacement in meters and t is the time in seconds. To find the force responsible, we need to take the second derivative of the equation with respect to time, which will give us the acceleration:
a = d²s/dt² = d²(5t + 2t²)/dt²
Differentiating the equation, we get:
a = 2
Since we know that force (F) is equal to mass (m) multiplied by acceleration, we can plug in our value for acceleration (a = 2) and mass (m = 10 kg) to find the magnitude of the force:
F = m * a = 10 * 2 = 20 N
So, the magnitude of the force responsible for your smooth moves is 20 N. Keep that force strong and keep grooving!
To find the magnitude of the force responsible for the motion, we need to use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
First, let's find the acceleration of the body by taking the second derivative of the equation of motion with respect to time (t).
Given:
s = 5t + 2t²
Taking the first derivative:
v = ds/dt
v = 5 + (2)(2t)
v = 5 + 4t
Taking the second derivative:
a = dv/dt
a = d(5 + 4t)/dt
a = 4
Now that we have the acceleration, we can find the magnitude of the force responsible for the motion by multiplying the mass of the body by its acceleration.
Given:
Mass (m) = 10 kg
Acceleration (a) = 4 m/s²
Using Newton's second law:
Force (F) = mass (m) x acceleration (a)
F = (10 kg)(4 m/s²)
F = 40 Newtons
Therefore, the magnitude of the force responsible for the motion is 40 Newtons.
50N
s=5t+2t²m
v=5+4tm/s
a=5m/s²
Given:
m=10kg
So,F=ma
F=10*5
F=50N