# Cars P and Q start the journey from the stationary at the same time and each accelerates with the acceleration  a  and 3ms ^ - 2. After 2 seconds, P leads Q by 6 m. Find  a ?

## A $4.5 m {s}^{- 2}$ B $5.0 m {s}^{- 2}$ C $5.5 m {s}^{- 2}$ D $6.0 m {s}^{- 2}$

Jul 28, 2018

D. $6 m {s}^{-} 2$

#### Explanation:

Distance $d = {V}_{0} t + \frac{1}{2} a {t}^{2}$

Car P has acceleration $a$
Car Q has acceleration $3 m {s}^{- 2}$
${V}_{0} = 0$ for both cars
$t = 2 s$

Distance traveled by car Q:
${d}_{Q} = 0 \cdot t + \frac{1}{2} \cdot 3 \cdot \left({2}^{2}\right) = 6$m

Distance traveled by car P:
${d}_{P} = 0 \cdot t + \frac{1}{2} \cdot a \cdot \left({2}^{2}\right) = 6 + 6 = 12$m

$\frac{4}{2} \cdot a = 12$

$a = 12 \cdot \frac{2}{4} = 6 m {s}^{-} 2$