Question

A racing car uniform acceleration of $4m{{s}^{-2}}$. What distance will it cover in 10 s after start?
A. 200 m
B. 80 m
C. 400 m
D. 40 m

Answer 1

Hint: Write down all the data given, also write down what is asked. Then write all the three equations of motion. And based on data given and quantity which is asked, select one equation and do calculation and find the distance.

Complete step by step answer:
Given data:
Initial velocity = 0 m/s
Acceleration = $4m{{s}^{-2}}$
Total time taken = 10 s
Distance = S =?
From second equation of motion
$\begin{align}
  & S=ut+\dfrac{1}{2}a{{t}^{2}} \\
 & t=10s,a=4m/{{s}^{2}} \\
 & S=0\times 10+\dfrac{1}{2}\times 4\times {{10}^{2}} \\
 & S=200m \\
\end{align}$
Hence, Distance it will cover in 10 second after start is 200m.

Additional Information:
Other equations of motion are as follows –
$\begin{align}
  & V=u+at \\
 & {{V}^{2}}={{u}^{2}}+2aS \\
\end{align}$
Here, V is the final velocity of the racing car.

Note: The distance can also be calculated by using below formulas
 $\begin{align}
  & V=u+at \\
 & {{V}^{2}}={{u}^{2}}+2aS \\
\end{align}$
Here, first V has to find by using $V=u+at$ then put the value of V in ${{V}^{2}}={{u}^{2}}+2aS$. And find distance.