# Mechanics - SUVAT Equations

> Source: https://ollybritton.com/notes/a-level/maths/topics/mechanics/suvat-equations/ · Updated: 2020-10-06 · Tags: mechanics, school, year-1

See [Physics - SUVAT Equations](https://ollybritton.com/notes/a-level/physics/topics/suvat-equations/), it's largely the same.

### Choosing an equation with no time

##### If you have two cars which decelerate the same amount ($a$) over the same distance ($s$), which SUVAT equation can you use??
$$
v^2 = u^2 + 2as
$$
^suvat-no-time-equation

##### Two cars, $A$ and $B$, have a $100ms^{-1}$ and $80ms^{-1}$ velocity respectively. Car $B$ reaches a final velocity of $0ms^{-1}$. Car $A$ reaches a final velocity of $x\\, ms^{-1}$. They decelerate the same amount ($a$) over the same distance ($s$). What two SUVAT equations can you come up with??
$$
0^2 = 80^2 + 2as
$$

$$
x^2 = 100^2 + 2as
$$
^two-car-equal-deceleration-system

### Acceleration due to gravity arithmetic

##### What is $9.8\times2$??
$$
19.6
$$
^nine-point-eight-times-two

##### What is $9.8\div2$??
$$
4.9
$$
^nine-point-eight-divided-by-two

### Equating velocities at a shared point

##### You are told that ![robot.png](https://ollybritton.com/assets/attachments/img/robot.png) It seems like there's one equation with two unknowns. How can you find $k$??
Use the fact that the velocity at $k$ must be equal for both curves.
^equate-velocities-to-find-shared-point

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