Interactive physics simulator
First Equation of Motion: v = u + at
The first equation of motion shows how final velocity depends on initial velocity, acceleration, and time when acceleration is constant.
First Equation of Motion Simulator
Use v = u + at for constant acceleration. This equation finds final velocity, not distance.
Live Result
- Initial velocity u
- 5 m/s
- Acceleration a
- 2 m/s²
- Time t
- 4 s
- Elapsed time
- 0 s
- Current velocity
- 5 m/s
- Final velocity v
- 13 m/s
- Direction
- positive direction
- Unit
- m/s
- Formula
- v = 5 + 2 x 4
What is v = u + at?
The equation v = u + at connects initial velocity, acceleration, and time to calculate final velocity. It is valid when acceleration is constant over the time interval.
Key Idea
The first equation of motion calculates final velocity when initial velocity, acceleration, and time are known.
- It works for constant acceleration.
- It shows how velocity changes with time.
- Positive acceleration increases velocity in the positive direction.
- Negative acceleration decreases velocity in the positive direction.
- If acceleration is zero, final velocity equals initial velocity.
- It does not directly calculate distance.
First Equation of Motion Formula
v = u + at
Final velocity = Initial velocity + Acceleration x Time
v is final velocity, u is initial velocity, a is acceleration, and t is time.
Use m/s for velocity, m/s² for acceleration, and seconds for time.
Rearranged forms
- u = v - at
- a = (v - u) / t
- t = (v - u) / a
Use a rearranged form only when the required variable is unknown and the other three values are known.
When to Use This Formula
Use v = u + at when:
- Acceleration is constant.
- Initial velocity is known.
- Acceleration is known.
- Time is known.
- Final velocity is required.
Do not use it alone when:
- You need distance or displacement.
- Acceleration is changing.
- Time is unknown and acceleration is zero.
- The motion is not uniformly accelerated.
Real-life Example of v = u + at
A small rocket starts from rest and accelerates at 3 m/s² for 5 seconds.
u = 0 m/s, a = 3 m/s², t = 5 s.
v = 0 + 3 x 5 = 15 m/s.
- A ball rolling down a slope speeds up with time.
- An elevator capsule slowing down has negative acceleration.
Solved Examples
An object starts from rest and accelerates at 2 m/s² for 6 s. Find final velocity.
- v = u + at
- v = 0 + 2 x 6
- v = 12 m/s
Answer: 12 m/s
A drone has initial velocity 5 m/s and acceleration 3 m/s² for 4 s. Find final velocity.
- v = u + at
- v = 5 + 3 x 4
- v = 17 m/s
Answer: 17 m/s
A ball moving at 20 m/s slows down with acceleration -4 m/s² for 3 s. Find final velocity.
- v = u + at
- v = 20 + (-4 x 3)
- v = 8 m/s
Answer: 8 m/s
A particle has initial velocity 6 m/s and acceleration 0 m/s² for 10 s. Find final velocity.
- v = u + at
- v = 6 + 0 x 10
- v = 6 m/s
Answer: 6 m/s
Common Mistakes
- Using the formula when acceleration is not constant.
- Forgetting that time must be in seconds.
- Forgetting acceleration unit is m/s².
- Mixing up initial velocity and final velocity.
- Forgetting the sign of acceleration.
- Writing v = u + a/t instead of v = u + at.
- Using this equation to directly calculate distance.
- Forgetting that negative velocity means opposite direction.
Quick Summary
- First equation of motion: v = u + at.
- It calculates final velocity.
- It works when acceleration is constant.
- u means initial velocity.
- v means final velocity.
- a means acceleration.
- t means time.
- Positive acceleration can increase velocity.
- Negative acceleration can reduce velocity or reverse direction.
Practice Questions
1. An object starts from rest and accelerates at 4 m/s² for 5 s. Find final velocity.
v = u + at = 0 + 4 x 5 = 20 m/s.
2. A drone moves at 10 m/s and accelerates at 2 m/s² for 3 s. Find final velocity.
v = 10 + 2 x 3 = 16 m/s.
3. A ball moves at 25 m/s and has acceleration -5 m/s² for 4 s. Find final velocity.
v = 25 + (-5 x 4) = 5 m/s.
4. If u = 8 m/s, a = 0 m/s², and t = 6 s, what is v?
v = 8 + 0 x 6 = 8 m/s.
5. Rearrange v = u + at to find acceleration.
Subtract u from both sides, then divide by t: a = (v - u) / t.
6. Does v = u + at work when acceleration is changing?
No. This equation is for constant acceleration only.
FAQ
Frequently Asked Questions
What is the first equation of motion?
The first equation of motion is v = u + at. It gives final velocity when initial velocity, acceleration, and time are known.
What does v mean in v = u + at?
v means final velocity.
What does u mean in v = u + at?
u means initial velocity.
What does a mean in v = u + at?
a means acceleration.
What does t mean in v = u + at?
t means time, usually measured in seconds.
When can I use v = u + at?
You can use it when acceleration is constant and you need final velocity.
Can v = u + at be used to find distance?
No. This equation directly finds final velocity, not distance. For distance, use another equation such as s = ut + 1/2at².
What happens if acceleration is zero?
If acceleration is zero, v = u. That means final velocity equals initial velocity.
Can final velocity be negative?
Yes. Negative final velocity means the object is moving in the negative direction according to the chosen coordinate system.
How does the simulator calculate final velocity?
The simulator uses the formula v = u + at and updates the result live when initial velocity, acceleration, or time changes.
Is this formula valid for changing acceleration?
No. The formula v = u + at is for constant acceleration only.
How do I find acceleration from v = u + at?
Rearrange the formula to a = (v - u) / t.