Please Help. A 5 kg object is propelled from rest at time t=0 by a net force F that always acts in the same direction. The magnitude of F in newtons is given as a function of t in seconds by F= 0.5t. What is the speed of the object at t =4s?

F=ma

.5t=m a

v= ds/dt
a= dv/dt

v= int a dt= int F/mass dt= INT .5t/m dt

v= 1/4 4^2/m=4/5 m/s check that.

Well, it seems like the object is about to go on quite the "t-speed" chase! Let me assist you with this physics problem, while trying to inject some humor into our calculations.

To find the speed of the object at t=4s, we need to find its acceleration first. Acceleration, as we may recall, is the rate at which an object's velocity changes over time.

Now, the net force F is given as 0.5t Newtons. As the object is a 5 kg mass, we can use Newton's second law, which states that F = ma, where F is the net force, m is the mass, and a is the acceleration.

Substituting the force and mass into the equation, we get 0.5t = 5a. Solving for a, we find that a = 0.1t.

Now, as the object is initially at rest (v=0) and we want to find its speed at t=4s, we can integrate the acceleration function from 0 to 4 to find the change in velocity.

Integrating a = 0.1t with respect to t, we get v = 0.1(0.5t^2)| from 0 to 4. Plugging in the values, we get v = 0.1(0.5*4^2) - 0.1(0.5*0^2).

Calculating that out, we find v = 0.1(0.5*16) - 0.1(0) = 0.1(8) = 0.8 m/s.

So, after all those calculations, we find that the speed of the object at t = 4s is 0.8 m/s. It's ready to speed up and go on its merry way!

Keep in mind that this answer assumes that the object moves in a straight line and that there are no other forces acting on it, other than the net force F mentioned in the problem.

To find the speed of the object at t=4s, we can use the equation for acceleration:

a = F/m

Here, F is the net force acting on the object and m is its mass.

Given that the mass of the object is 5 kg and the magnitude of the force is given by F = 0.5t, we can substitute these values into the equation and solve for the acceleration.

a = (0.5t) / m

a = (0.5 * 4) / 5

a = 2 / 5

a = 0.4 m/s^2

Now, we can use the equation for constant acceleration to find the speed of the object at t=4s:

v = u + at

Given that the object is initially at rest (u=0), we can simplify the equation:

v = 0 + (0.4 * 4)

v = 1.6 m/s

Therefore, the speed of the object at t=4s is 1.6 m/s.

To find the speed of the object at t=4s, we need to determine the acceleration of the object using the net force applied to it and then use that acceleration to calculate its speed.

The acceleration of an object can be found using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).

In this case, the net force F is given as a function of time (F = 0.5t) and the mass of the object is 5 kg. So, we can substitute these values into the equation:

0.5t = ma

Since we know the mass m = 5 kg, we can rearrange the equation to solve for acceleration a:

a = (0.5t)/m

Now, we can substitute the time t = 4s into the equation to find the acceleration at t = 4s:

a = (0.5 * 4) / 5
a = 0.4 m/s^2

Now that we have the acceleration, we can calculate the speed of the object at t = 4s. The speed of an object can be found using the equation of motion:

v = u + at

Here, 'u' represents the initial velocity of the object, and since the object is propelled from rest, u is 0. So, the equation becomes:

v = 0 + (0.4 * 4)
v = 1.6 m/s

Therefore, the speed of the object at t = 4s is 1.6 m/s.

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