I need help with this question with explanation. Thanks
A particle of mass m starts from rest at position x = 0 and time t = 0. It moves along the positive x-axis under the influence of a single force Fx = bt, where b is a constant. The velocity v of the particle is given by
A) bt/m
B) bt2/2m
C) bt2/m
D) b√t/m
E) b/mt
Hello, I was looking at this problem and probably can explain what is going on
so what you did is you tried to substitute acceleration for change in velocity/ change in time and got (bt^2/M) just like me, well you only found change of velocity, NOT velocity
your answer should be B
F= bt
ma=bt //replace Force with ma
a=bt/m // get a by itself
v=bt^2/2m // take the integral of both sides to find your velocity and answer (remember b and m are constants)
I hope this helped
F = bt
ma = bt
a = (bt)/m
Note that you can not use the standard kinematics equations because the acceleration is not constant! The acceleration is a function of time; you need to use an integral.
∫(bt)/m dt - acceleration times time, but the acceleration isn't constant.
= (bt^2)/(2m)
Well, isn't it interesting that this particle is moving along the positive x-axis? It's like it's refusing to go backwards, just like my old toaster - once it pops, there's no going back!
Now, let's take a look at the given force Fx = bt, where b is a constant. This force is increasing linearly with time, just like my excitement when I see a plate of freshly baked cookies!
Since force is defined as mass times acceleration (F = ma), we can rearrange the equation to find acceleration a = F/m. So, in this case, the acceleration a is equal to bt/m.
Now, to find the velocity v of the particle, we know that velocity is the integral of acceleration with respect to time. Integrating the acceleration bt/m with respect to time, we get (bt^2)/(2m), which is option B!
So, the correct answer is option B) bt^2/2m. And just like that, we've solved the question! Keep sending in those brain teasers, I'm always here to provide a little humor along the way!
To find the velocity of the particle as a function of time, we can use the equation F = ma, where F is the force, m is the mass of the particle, and a is the acceleration.
In this case, the force is given by Fx = bt, where b is a constant. Since Fx = ma, we have:
bt = ma
To solve for acceleration, we can rearrange the equation as follows:
a = bt/m
Now, we know that acceleration is the derivative of velocity with respect to time. So, we can integrate the equation to find the velocity as a function of time:
∫dv = ∫(bt/m)dt
This simplifies to:
v = (bt^2)/(2m) + C
Here, C is a constant of integration, which we'll determine later. So, the correct answer is B) bt^2/(2m).
Hello, I was looking at this problem and probably can explain what is going on
so what you did is you tried to substitute acceleration for change in velocity/ change in time and got (bt/M) just like me, well you only found change of velocity, NOT velocity
your answer is bt^2/2m (which is NOT listed above)
F= bt
ma=bt //replace Force with ma
a=bt/m // get a by itself
v=bt^2/2m // take the integral of both sides to find your velocity and answer (remember b and m are constants)
I hope this helped
this is analogous to the relationship between
... acceleration, velocity, and distance
acceleration is velocity changing with time ... v = a t
... and velocity is distance changing with time ... d = v t
... so , d = 1/2 a t^2
in this case
... force is acceleration changing with time ... a = (b/m) t
... and acceleration is velocity changing with time ... v = a t
... so , v = 1/2 (b/m) t^2