# Trying to find HOW to get the velocity.

• JohnTheGreat101
In summary, the conversation discusses a practice problem involving calculating the initial velocity of a block with a dart, taking into account friction and the rolling resistance coefficient. The conversation also brings up some oddities and clarifies the necessary calculations.
JohnTheGreat101
Homework Statement
Suppose a 15.0 g dart is fired into a wooden block that is mounted on wheels with a total
mass of 10.0 kg. The time required for the block to travel a distance of 45.0 cm is
measured after the dart lodges into the block. This can easily be accomplished with a
pair of photocells and an electric clock. If the coefficient of friction between the
wheels and floor is 0.1435 and the measured time to come to a stop is .80 seconds, what
is the muzzle velocity of the dart? (assume no drag force on the dart before it hits the
block).
Relevant Equations
x= vt + 1/2 at^2
m1v1=m2v2
This is a practice problem so I know that the answer is 750 m/.s. Not totally sure what to do with the friction or if any of my listed equations are relevant here but here goes what I've tried:

.45 kg = v(0.8 sec) + 1/2(-9.8 *0.1435) * (0.8)^2

.45 kg = v(0.8) + 1/2(-1.4063) * 0.64
.45=v(0.8) - 0.450015
0.900016= V(0.8)
V does not equal 1.12 m/s

You only calculated the initial velocity of the block with the dart in it. You still need to calculate initial velocity of dart. You have also written some units incorrectly, but it does not effect the math. The force of friction is -.1435mg so the acceleration is -.1435g.

There are some oddities with the question.
We are given the "coefficient of friction". Assuming the wheels are free to rotate, the friction will be static, and its coefficient irrelevant. So presumably they mean the rolling resistance coefficient.
It says the time to travel a stated distance is measured, but at that point in the text does not specify that time.
Later, it gives the time to come to a stop. Are we supposed to assume these refer to the same event, i.e. it comes to a stop at the given distance?
It seems so, since on that basis we can calculate the rolling resistance, and it is indeed the value given. So whoever set the question must have been aware it was redundant information. Unusual.

JohnTheGreat101 said:
.45 kg = v(0.8 sec) + 1/2(-9.8 *0.1435) * (0.8)^2
.45cm.

While I typed all that, @caz beat me to pointing out your error.

Last edited:
caz said:
You only calculated the initial velocity of the block with the dart in it. You still need to calculate initial velocity of dart. You have also written some units incorrectly, but it does not effect the math. The force of friction is -.1435mg so the acceleration is -.1435g.
I see so then I would just apply the equation: m1v1=m2v2 and solve for V1?

Yes.

## 1. What is velocity?

Velocity is the rate of change of an object's position with respect to time. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position by the change in time. This can be represented by the formula v = Δx/Δt, where v is velocity, Δx is change in position, and Δt is change in time.

## 3. What units is velocity measured in?

Velocity is commonly measured in meters per second (m/s) or kilometers per hour (km/h). However, it can also be measured in other units such as feet per second (ft/s) or miles per hour (mph).

## 4. How does velocity differ from speed?

Velocity and speed are often used interchangeably, but they are actually different quantities. While velocity takes into account both the magnitude and direction of an object's motion, speed only measures the magnitude or how fast an object is moving.

## 5. What factors affect an object's velocity?

An object's velocity can be affected by various factors such as its initial speed, acceleration, and any external forces acting upon it. Other factors like air resistance, friction, and gravity can also impact an object's velocity.

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