# If an object is moving at 8 m/s and accelerates to 32 m/s over 6 seconds, what was the object's rate of acceleration?

Jun 29, 2018

$4 \setminus {\text{m/s}}^{2}$

#### Explanation:

Well, the object changed its velocity by $32 \setminus \text{m/s"-8 \ "m/s}$ over $6$ seconds.

Acceleration is given by the equation:

$a = \frac{{s}_{f} - {s}_{i}}{t}$

where:

• ${s}_{f} , {s}_{i}$ are the final and initial speeds, respectively

• $t$ is the time taken

So, we get:

$a = \left(32 \setminus \text{m/s"-8 \ "m/s")/(6 \ "s}\right)$

$= \left(24 \setminus \text{m/s")/(6 \ "s}\right)$

$= 4 \setminus {\text{m/s}}^{2}$

Jun 29, 2018

The acceleration is $= 4 m {s}^{-} 2$

#### Explanation:

The initial velocity is $u = 8 m {s}^{-} 1$

The final velocity is $v = 32 m {s}^{-} 1$

The time is $t = 6 s$

Apply the equation of motion

$v = u + a t$

The acceleration is

$a = \frac{v - u}{t} = \frac{32 - 8}{6} = \frac{24}{6} = 4 m {s}^{-} 2$

Jun 29, 2018

Rate of acceleration $a = 6$ m/ ${s}^{2}$

#### Explanation:

$v = u + a t$

$u = 8$ m/s, $v = 32$ m/s, $t = 6$ sec

$a = \frac{v - u}{t} = \frac{32 - 8}{6} = 4$ m / ${s}^{2}$