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Kinematics (SUVAT) calculator

Kinematics calculator for the SUVAT equations: enter three of displacement, initial and final velocity, acceleration and time to get the other two.

업데이트 검증한 예제: 6

Use −9.80665 m/s² for free fall with up as positive
시도하기
Final velocity v
m/s
Final velocity v: 20 m/s
유효 자릿수: 6; 가장 가까운 값, 중간값은 0에서 먼 쪽으로
Displacement s
100m
Initial velocity u
0m/s
Acceleration a
2m/s²
Time t
10s

Displacement is 100 m and final velocity is 20 m/s. The shaded area under the velocity line equals the displacement.

Velocity against time

051015200246810Time (s)Velocity (m/s)t = 10 s

Displacement against time

02550751000246810Time (s)Displacement (m)
계산 방법 S

  1. Knowns in SI units

    u=0 m/s,a=2 m/s2,t=10 su = 0\ \mathrm{m/s},\quad a = 2\ \mathrm{m/s^2},\quad t = 10\ \mathrm{s}

  2. Final velocity

    v=u+at=0+(2)(10)=20 m/sv = u + at = 0 + (2)(10) = 20\ \mathrm{m/s}

  3. Displacement

    s=ut+12at2=(0)(10)+12(2)(10)2=100 ms = ut + \tfrac12 a t^2 = (0)(10) + \tfrac12(2)(10)^2 = 100\ \mathrm{m}

Kinematics (SUVAT) calculator 소개

Motion with constant acceleration is described by five quantities: displacement s, initial velocity u, final velocity v, acceleration a and time t. Each of the five SUVAT equations leaves one of them out, so any three known values fix the other two. When time is unknown, s = ut + ½at² is a quadratic and can have two valid roots.

Physics students use it for braking, free-fall and launch problems. With the defaults, an object starting from rest and accelerating at 2 m/s² for 10 s reaches 20 m/s and covers 100 m. A ball thrown straight up at 20 m/s passes 15 m twice, at 0.99 s and 3.09 s, and both times are listed.

Acceleration must stay constant and the motion must lie along one line. Values are signed: choose a positive direction and give opposing quantities a minus sign, so free fall with up as positive uses a = −9.80665 m/s².

계산 예제

From rest at 3 m/s² for 8 s

Find
s and v (know u, a, t)
Initial velocity u
0 m/s
Acceleration a
3 m/s²
Time t
8 s
Final velocity v
24 m/s
Displacement s
96 m

검증 출처: Python 3.8 decimal: v = 0 + 3·8 = 24; s = ½·3·8² = 96

Ball thrown up at 20 m/s passes 15 m twice

Find
v and t (know s, u, a)
Displacement s
15 m
Initial velocity u
20 m/s
Acceleration a
-9.81 m/s²
Time t
0.990719 s
Second time (other root)
3.08675 s
Final velocity v
10.2811 m/s
Final velocity at the second time
-10.2811 m/s

검증 출처: Python 3.8 decimal: t = (20 ∓ √(400 − 2·9.81·15))/9.81 = 0.9907186…, 3.0867534…; v = 20 − 9.81t = ±10.2810505…

Car braking from 10 m/s to rest in 50 m

Find
a and t (know s, u, v)
Displacement s
50 m
Initial velocity u
10 m/s
Final velocity v
0 m/s
Time t
10 s
Acceleration a
-1 m/s²

검증 출처: Python 3.8 decimal: t = 2s/(u+v) = 10; a = (0 − 100)/(2·50) = −1

Zero acceleration (uniform motion)

Find
v and t (know s, u, a)
Displacement s
100 m
Initial velocity u
5 m/s
Acceleration a
0 m/s²
Time t
20 s
Final velocity v
5 m/s

검증 출처: Python 3.8 decimal: t = s/u = 20 (linear case of ½at² + ut − s = 0)

자주 묻는 질문

What does SUVAT stand for?

SUVAT names the five quantities in the constant-acceleration equations: s for displacement, u for initial velocity, v for final velocity, a for acceleration and t for time. The equations are v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t and s = vt − ½at². Each omits a different variable, so you pick the one that leaves out the quantity you neither know nor need.

When can you use the SUVAT equations?

Only when acceleration is constant and the motion is in a straight line. Free fall near the Earth's surface qualifies while air resistance is small; standard gravity is 9.80665 m/s², the value adopted by the 3rd General Conference on Weights and Measures in 1901. A skydiver nearing terminal velocity, or a car whose acceleration fades as it gains speed, needs calculus or a numerical model instead.

How do you calculate stopping distance with SUVAT?

Set the final velocity to zero in v² = u² + 2as, which gives s = u² ÷ (2 × deceleration). A car braking from 10 m/s (36 km/h) at 1 m/s² stops in 50 m after 10 s. Doubling the starting speed quadruples the braking distance. The distance covered during the driver's reaction time comes on top and is uniform motion, s = ut.

Why are there two answers for time?

When time is the unknown, s = ut + ½at² is a quadratic in t and can have two positive roots. A ball thrown upward at 20 m/s with a = −9.81 m/s² is 15 m above the start at 0.99 s on the way up and again at 3.09 s on the way down, moving at 10.28 m/s each time but in opposite directions. Negative roots are dropped because time starts at zero.

What value of g should I use?

Use 9.80665 m/s², the defined standard gravity, unless the problem states another value; many textbooks round it to 9.81 or 9.8 m/s². Real sea-level gravity varies with latitude, from about 9.780 m/s² at the equator to 9.832 m/s² at the poles in the WGS 84 model. That spread changes answers by about 0.5%.

“Kinematics (SUVAT) calculator”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 6. 예를 들어 “From rest at 3 m/s² for 8 s”은 Python 3.8 decimal: v = 0 + 3·8 = 24; s = ½·3·8² = 96와 대조해 확인합니다.

이 계산 방법의 출처는 무엇인가요?

OpenStax University Physics Volume 1, §3.4 Motion with constant acceleration; HyperPhysics — Motion equations for constant acceleration.

이 계산기 소개

v=u+at,s=ut+12at2,v2=u2+2as,s=12(u+v)t,s=vt−12at2v = u + at,\quad s = ut + \tfrac12at^2,\quad v^2 = u^2 + 2as,\quad s = \tfrac12(u+v)t,\quad s = vt - \tfrac12at^2

출처

  1. OpenStax University Physics Volume 1, §3.4 Motion with constant acceleration
  2. HyperPhysics — Motion equations for constant acceleration

출처와 대조하여 검증

이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 6개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.

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