An object with a mass of 0.75 kg is projected over a horizontal surface with a speed of 2.5 m/s. It then comes to rest after 3.0 s.

Question

Illustrate a minimalist abstract image showing the concept of a physics problem. Visualize an object with a defined mass, represented by a simple geometric shape, being projected across a horizontal surface. This horizontal surface should be clear and sleek, affording plenty of space for the object to travel. Depict the object initially in a state of motion, with subtle visual cues like motion lines to indicate its speed. Then, show the same object at rest, signalling the end of its motion. The overall perspective should not include any text but should visually depict a change in kinetic energy.

An object with a mass of 0.75 kg is projected over a horizontal surface with a speed of 2.5 m/s. It then comes to rest after 3.0 s.

(a) How much is the change in kinetic energy of the object.

Answer 1

The change in kinetic energy of the object is -19.375 J.

Answer 2

Well, well, well, if it isn't Mr. Speedy McSpeedster! Let's calculate that change in kinetic energy, shall we?

To calculate the change in kinetic energy, you need to subtract the initial kinetic energy from the final kinetic energy. Since the object comes to rest, its final kinetic energy is zero.

Now, let's get down to business. The formula for kinetic energy is KE = (1/2)mv^2, where m is the mass and v is the velocity. Plug in the given values, and we get:

Initial kinetic energy (KEi) = (1/2)(0.75 kg)(2.5 m/s)^2

Simplify that equation, and voila! You have the initial kinetic energy.

But wait...we need to calculate the final kinetic energy as well. Since the object comes to rest, its final kinetic energy (KEf) is zero.

Finally, to find the change in kinetic energy, we'll simply subtract the final kinetic energy from the initial kinetic energy:

Change in kinetic energy = KEf - KEi

And there you have it, the answer to your question!

Answer 3

To find the change in kinetic energy, we need to calculate the initial and final kinetic energy of the object.

The formula to calculate kinetic energy is:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass (m) = 0.75 kg
Initial velocity (vi) = 2.5 m/s
Final velocity (vf) = 0 m/s (since the object comes to rest)

Let's calculate the initial kinetic energy (KEi) using the given values:

KEi = (1/2) * m * vi^2
KEi = (1/2) * 0.75 kg * (2.5 m/s)^2

Calculating KEi:
KEi = (1/2) * 0.75 kg * 6.25 m^2/s^2
KEi = 2.34375 Joules

Now, let's calculate the final kinetic energy (KEf):

KEf = (1/2) * m * vf^2
KEf = (1/2) * 0.75 kg * (0 m/s)^2

Calculating KEf:
KEf = (1/2) * 0.75 kg * 0 m^2/s^2
KEf = 0 Joules

We can now find the change in kinetic energy (ΔKE) by subtracting the final kinetic energy from the initial kinetic energy:

ΔKE = KEf - KEi
ΔKE = 0 Joules - 2.34375 Joules
ΔKE = -2.34375 Joules

Therefore, the change in kinetic energy of the object is -2.34375 Joules.

Answer 4

To calculate the change in kinetic energy, we need to find the initial kinetic energy (Ki) and the final kinetic energy (Kf) and then subtract Ki from Kf.

The formula for calculating kinetic energy is:
Kinetic Energy (K) = 0.5 * mass * (velocity)²

Given:
Mass (m) = 0.75 kg
Initial speed (vi) = 2.5 m/s
Time taken (t) = 3.0 s

To find the initial kinetic energy (Ki):
Ki = 0.5 * m * (vi)²

Plugging in the values:
Ki = 0.5 * 0.75 kg * (2.5 m/s)²

Now, let's calculate the final speed (vf) using the equation of motion:
vf = vi + a * t

Since the object comes to rest, vf = 0.

So, 0 = 2.5 m/s + a * 3.0 s

Solving for acceleration (a):
a * 3.0 s = -2.5 m/s
a = -2.5 m/s / 3.0 s

Now, we can use the equation of motion to find the distance traveled (d):
d = vi * t + 0.5 * a * (t)²

Plugging in the values:
d = 2.5 m/s * 3.0 s + 0.5 * (-2.5 m/s / 3.0 s) * (3.0 s)²

Finally, let's calculate the final kinetic energy (Kf):
Kf = 0.5 * m * (vf)²

Plugging in the values:
Kf = 0.5 * 0.75 kg * (0 m/s)²

Now, subtract Ki from Kf to find the change in kinetic energy:
Change in Kinetic Energy = Kf - Ki

It is important to note that since the object comes to rest, the final kinetic energy (Kf) will be zero. Therefore, the change in kinetic energy will be negative and equal to the initial kinetic energy (Ki).