Can someone please help me solve the formula below for v1? a = v1 – v0t
The Correct Answer and Explanation is:
To solve the equation a=v1−v0ta = v_1 – v_0 ta=v1−v0t for v1v_1v1, follow these steps:
1. Understand the equation
The equation provided relates acceleration aaa to the initial velocity v0v_0v0, the final velocity v1v_1v1, and time ttt. It’s a fundamental equation in kinematics, often used to describe the motion of an object with constant acceleration.
2. Rearrange to isolate v1v_1v1
Start with the equation: a=v1−v0ta = v_1 – v_0 ta=v1−v0t
We want to solve for v1v_1v1. To isolate v1v_1v1, add v0tv_0 tv0t to both sides of the equation: a+v0t=v1a + v_0 t = v_1a+v0t=v1
Thus, the final velocity v1v_1v1 is: v1=a+v0tv_1 = a + v_0 tv1=a+v0t
3. Explanation of the result
The equation v1=a+v0tv_1 = a + v_0 tv1=a+v0t tells us that the final velocity v1v_1v1 is equal to the initial velocity v0v_0v0 plus the acceleration aaa multiplied by the time ttt. This makes sense in kinematics because if an object starts with an initial velocity v0v_0v0, its velocity after time ttt will change due to the acceleration aaa. The term v0tv_0 tv0t accounts for the distance the object would have traveled at the initial velocity, while the term aaa reflects how the velocity changes due to the acceleration over time.
4. Units consistency
Make sure the units are consistent when applying this formula. Typically:
- aaa (acceleration) is measured in meters per second squared (m/s²),
- v0v_0v0 (initial velocity) and v1v_1v1 (final velocity) are measured in meters per second (m/s),
- ttt (time) is measured in seconds (s).
When all units are in their standard SI forms, the result will give you a final velocity in meters per second.
This is a simple but powerful formula to calculate the final velocity when you know the acceleration, initial velocity, and the time interval.
