Solving SAT Physics: Momentum of Block Starting from Rest at 5s

[spyroarcher]

Homework Statement

If the block starts from rest, its momentum at 5 seconds is...

Homework Equations

p=mv
F=ma
v=at

The Attempt at a Solution

When I thought about it, I was thinking about p=mv, and I had to substitute v to get a desirable answer. So I did p=m(at). However I only know the time, and I know the answer is 10 kg m/s, but I am not sure how to do it. Thanks in advance.

 

[Mindscrape]

"If the block starts from rest, its momentum at 5 seconds is..."

Is that the full question? If so, there is no answer.

 

[spyroarcher]

Yes that is the full question, if it is impossible, how would the book get 10?
It also said p=F(change in T) for the answer

 

[Mindscrape]

Sure, F=dp/dt, so ∆p=∫Fdt. If you have a constant force of 2N acting on the particle you will get ∆p=F∆t=2*5=10 kgm/s, but I don't see anything about that.

 

[rwisz]

I would approach this problem by first understanding the concept of momentum and how it is related to the mass and velocity of an object. The equation p=mv tells us that the momentum of an object is equal to its mass multiplied by its velocity. In this case, the block is starting from rest, which means its initial velocity is 0 m/s. We also know that the block has a mass of 10 kg.

Using the equation v=at, we can calculate the final velocity of the block at 5 seconds. Since the block is starting from rest, its initial velocity is 0 m/s and the acceleration is constant at all times, we can simply use the equation v=at to find the final velocity.

v=at
v=(5s)(a)
v=5a

Now, we can substitute this value for velocity into the equation p=mv.

p=mv
p=(10kg)(5a)
p=50a

Finally, to find the momentum at 5 seconds, we need to know the value of acceleration. This can be found by using the equation F=ma, where F is the force acting on the block. If we assume that there is a constant force acting on the block, we can find the acceleration by dividing the force by the mass.

F=ma
a=F/m

Substituting this value for acceleration into our equation for momentum, we get:

p=50(F/m)

Since we know that the mass of the block is 10 kg, we can simplify this equation to:

p=5F

This tells us that the momentum of the block at 5 seconds is directly proportional to the force acting on it. Therefore, if we know the force acting on the block, we can easily calculate its momentum at 5 seconds.

In summary, to solve this problem, we used the equations p=mv, v=at, and F=ma to find the momentum of the block at 5 seconds. By understanding the concepts of momentum, mass, velocity, acceleration, and force, we were able to use these equations to arrive at a solution.