# If an object with uniform acceleration (or deceleration) has a speed of 2 m/s at t=0 and moves a total of 90 m by t=6, what was the object's rate of acceleration?

May 30, 2017

The rate of acceleration is $= 4.33 m {s}^{-} 2$

#### Explanation:

The initial speed is $u = 2 m {s}^{-} 1$

The distance is $s = 90 m$

The time is $t = 6 s$

The acceleration is a=?

We apply the equation of motion

$s = u t + \frac{1}{2} a {t}^{2}$

Therefore,

$\frac{1}{2} a {t}^{2} = s - u t$

$a = \frac{s - u t}{\frac{1}{2} {t}^{2}}$

$= \frac{90 - 6 \cdot 2}{\frac{1}{2} \cdot {6}^{2}}$

$= \frac{78}{18}$

$= 4.33 m {s}^{-} 2$