Question

A racing car has uniform acceleration of 4 ms-2. What distance will it cover in 10 seconds after the start?
A. 100 m
B. 300 m
C. 200 m
D. 400 m

Answer 1

Hint: Use Newton’s laws of motion relating initial velocity, acceleration, distance and time.

Formula used: $s=ut+\dfrac{1}{2}a{{t}^{2}}$
Here,
$s$ is the displacement
$u$ is the initial velocity
$t$ is the time
$a$ is the acceleration

Complete step by step solution:
Given
     $a$ = 4ms-2
     $t$ =10 seconds
     $u$ =0 (the car starts from rest with uniform acceleration)
Substituting it in the formula,
     $\begin{align}
  & s=0\times 10+\dfrac{1}{2}\times 4\times {{10}^{2}}\text{ m} \\
 & s=200\text{ m} \\
\end{align}$

The correct answer is option C.

Additional information: A body is said to be moving with constant acceleration if the change in velocity is constant each second.
Displacement can also be calculated by calculating the area of a velocity-time graph.

Note: The final velocity after travelling 200 m can be calculated as

     $\begin{align}
  & {{v}^{2}}-{{u}^{2}}=2as \\
 & v=\sqrt{2\times 4\times 200}\text{ m}{{\text{s}}^{-}}^{1}=40\text{ m}{{\text{s}}^{-}}^{1} \\
\end{align}$