Question

A car moving with a constant acceleration covers $24\mathrm{m}$ in $4s$ and $21\mathrm{m}$ in the next $2s$. What is the initial velocity of the car?

• A. $3km{h}^{-1}$
• B. $3m{s}^{-1}$
• C. $1.5km{h}^{-1}$
• D. $1.5m{s}^{-1}$

Answer 1

The correct option is B

$3m{s}^{-1}$

Step 1: Given Data

u= initial velocity,

a= acceleration

Step 2:Calculation

1. First 4 seconds
   $$\begin{gathered} 24=4u+\frac{1}{2}a\times {\left(4\right)}^2 \\ 24=4u+8a \\ 6=u+2a------\left(1\right) \end{gathered}$$
2. First 6 seconds
   $$\begin{gathered} 24+21=ut+\frac{1}{2}a{\left(6\right)}^2 \\ 45=u\left(6\right)+18a----\left(2\right) \end{gathered}$$
3. 2 - 6(1)
   $$\begin{gathered} 45-36=18a-12a \\ 9=6a \\ \frac{3}{2}m{s}^{-2}=a \end{gathered}$$

Substituting in equation 1)

$$\begin{gathered} 6=u+3 \\ 3m{s}^{-1}=u \end{gathered}$$

Hence, Option B is the correct answer.