Question

If a car at rest accelerates uniformly to a speed of 144 km/hr in 20s, then it covers a distance of :-
A. 20 m
B. 400 m
C. 1440 m
D. 2880 m

Answer 1

Hint: We are given that a car which is at rest accelerates uniformly. We have to find out the covered distance. As the acceleration of a body is constant and the motion is a straight line. So we used Newton’s first law of motion to solve this question. By putting the values we get the value of v,u and t we get the value of a and then by putting all the values we will be able to find the distance covered.

Formula used:
The equations of motion are,
$v = u + at$ and $s=ut+\dfrac{1}{2}a{{t}^{2}}$
Here, $v$= Final velocity
$u$= initial velocity
$a$= acceleration
$t$ = time

Complete step by step solution:
Given the car at rest accelerates uniformly
So the initial velocity of the car is u = 0
And the final velocity, $v = 144\,km/hr = 144\times \dfrac{5}{18}=40\,m/s$
Time taken, t = 20 s
Now we have a formula of velocity which is $v = u + at$.
Now we find out the value of a from the above formula, we get
$a=\dfrac{v-u}{t}$

Now we put the values of v, u and t, we get
$a=\dfrac{40-0}{20}$
$\Rightarrow a = 2\,m/{{s}^{2}}$
Now we know the formula of covered distance is
$s=ut+\dfrac{1}{2}a{{t}^{2}}$
Now we put the values in the above equation and we get
$s=0+\dfrac{1}{2}a{{t}^{2}}$
$\Rightarrow s=\dfrac{1}{2}\times 2\times {{(20)}^{2}}$
$\therefore s = 400\,m$
Hence, it covers a distance of 400 m.

Hence, option B is the correct answer.

Note: As per Newton's first law of motion, any object that doesn’t feel any net force will continue to go in a straight line with a perpetual velocity until it is subjected to net force. Also, kinematics equations of motion define the fundamental idea of an object's motion, such as its location, velocity, or acceleration at various intervals.