Question

What is the acceleration of a body that goes from `"40 m/s"` to rest over a distance of `"20/100 m"`?

Answer 1

`-4000ms^-2`
`-ve` sign shows that it is retardation or deceleration.

Explanation:

Th kinematic equation connecting quantities of interest is
`v^2-u^2=2as`
where `v` is final velocity, `u` is initial velocity, `a` being acceleration and `s` distance moved.

Inserting given values in the equation in SI units, we get,
`0^2-40^2=2a20/100`
Solving for `a`
`a=-40^2xx100/40`
`a=-4000ms^-2`
`-ve` sign shows that it is retardation or deceleration.

Answer 2

The acceleration is `-4000` `"m/s"^2"`.

The acceleration is negative because the object slowed to a stop. This is a negative acceleration, sometimes called deceleration (but not in Physics).

Explanation:

Use the equation:

`v_f^2=v_i^2+2ad`,

where:

`v_f` is the final velocity, `v_i` is the initial velocity, `a` is the acceleration, and `d` is the distance.

Known

`v_f="0 m/s"`

`v_i="40 m/s"`

`d="20/100 m"`

Unknown

acceleration, `a`

Solution

Rearrange the equation to isolate `a`. Plug in the known values and solve.

`a=(v_f^2-v_i^2)/(2d)`

`a=((0)-(40"m"/"s")^2)/(2*20/100"m")="`

`a=(-1600"m"^2/"s"^2)/(40/100"m")="` `larr` Invert fraction and multiply.

`a=-1600color(red)cancel(color(black)("m"))^1/"s"^2xx100/(40color(red)cancel(color(black)("m")))=-4000` `"m/s"^2"`

The acceleration is negative because the object slowed to a stop. This is a negative acceleration, sometimes called deceleration (but not in Physics).