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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.

更新于 已验证的示例：6

Use −9.80665 m/s² for free fall with up as positive
试一试
Final velocity v
m/s
Final velocity v: 20 m/s
有效数字：6；取最近值，等距时远离零
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)
计算方法 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}

关于Kinematics (SUVAT) calculator

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.

计算示例

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

核验来源：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

核验来源：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

核验来源：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

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

常见问题

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”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：6。 例如，“From rest at 3 m/s² for 8 s”根据Python 3.8 decimal: v = 0 + 3·8 = 24; s = ½·3·8² = 96进行核验。

这种方法出自哪里？

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

关于此计算器

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

来源

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

已对照来源验证

此计算器包含 6 个已解示例，答案来自独立来源。这些示例会在测试套件中运行，你也可以在此运行验证。

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