Technology
Calculating Acceleration of a Crate Pulled Horizontally
Calculating Acceleration of a Crate Pulled Horizontally
A crate, being pulled horizontally by a force of 200 N, accelerates from rest to a speed of 10.0 m/s in 2.0 seconds. To find the acceleration of the crate, we can use the formula for acceleration:
Acceleration (a):
a frac{{Delta v}}{{Delta t}}
where]
- a is the acceleration
- Delta v is the change in velocity
- Delta t is the change in time.
Given Values:
Initial velocity, v_0 0 m/s (since the crate starts from rest) Final velocity, v_f 10.0 m/s Time interval, Delta t 2.0 sNow, let's calculate the change in velocity:
Delta v v_f - v_0 10.0 m/s - 0 m/s 10.0 m/s
Now, plug these values into the acceleration formula:
a frac{10.0 m/s}{2.0 s} 5.0 m/s^2
Additional Formulas
Another way to find acceleration is using the formula for final velocity:
v u at
Where:
v is the final velocity u is the initial velocity a is the acceleration t is the timeUsing the same values:
10 m/s 0 m/s a * 2 s
a frac{10 m/s}{2 s} 5 m/s^2
Again, we confirm the acceleration is 5 m/s2.
Acceleration as the Rate of Change of Velocity
Acceleration is defined as the rate of change of velocity with respect to time. It indicates how much the velocity of a body changes in a given time interval.
In this example, we have:
Initial velocity, u 0 m/s Final velocity, v 10 m/s Time interval, t 2.0 sSo, the acceleration can be calculated as:
a frac{{v - u}}{{t}} frac{{10 m/s - 0 m/s}}{{2.0 s}} frac{{10 m/s}}{{2.0 s}} 5 m/s^2
Thus, the acceleration is 5 m/s2.
Conclusion
Understanding and calculating acceleration is crucial in physics, especially when dealing with the motion of objects under the influence of force. This example demonstrates how to apply the basic principles of kinematics to solve problems related to acceleration.