# If an object with uniform acceleration (or deceleration) has a speed of 12 m/s at t=0 and moves a total of 145 m by t=15, what was the object's rate of acceleration?

Jun 20, 2018

The deceleration is $= 0.31 m {s}^{-} 2$

#### Explanation:

Apply the equation of motion

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

The initial velocity is $u = 12 m {s}^{-} 1$

The distance is $s = 145 m$

The time is $t = 15 s$

Therefore,

$145 = 12 \times 15 + \frac{1}{2} a \times {15}^{2}$

$\frac{1}{2} a \cdot 225 = 145 - 180 = - 35$

$a = - 2 \cdot \frac{35}{225} = - 0.31 m {s}^{-} 2$