Question

A truck starts from rest with an acceleration of $1.5{\text{m/s}}^2$ while a car $150\text{m}$ behind starts from rest with an acceleration of $2{\text{m/s}}^2$. What is the distance travelled by the car before it gets side by side to the truck?

• A. $300\text{m}$
• B. $400\text{m}$
• C. $600\text{m}$
• D. $800\text{m}$

Answer 1

The correct option is C $600\text{m}$

Let $a_1$ and $a_2$ be the accelerations of truck and the car respectively.
Let $d$ be the distance travelled by the truck before it gets side by side to the car
Therefore, distance travelled by the car before it gets side by side to the truck $=d+150$
Using second equation of motion for truck, we get
$d=u_{1}t+\frac{1}{2}{a}_1{t}^2$
As the truck starts from rest
$\Rightarrow u_1=0$
$\Rightarrow d=\frac{1}{2}\times 1.5\times t^2.....\text{(i)}$
Using second equation of motion for car, we get
$d+150=u_{2}t+\frac{1}{2}{a}_2{t}^2$
As the car also starts from rest
$\Rightarrow u_2=0$
$\Rightarrow d+150=\frac{1}{2}\times 2\times t^2.....\text{(ii)}$
On solving $\text{(i)}$ and $\text{(ii)}$, we get
$t^2=600{\text{s}}^2,d=450\text{m}$
$\therefore$ Distance travelled by the car to get side by side to the truck $=d+150=600\text{m}$