Question

Two cars A and B start from the same starting point. A is starting from rest and moving with constant acceleration $2m/{s^2}$ and B is starting with a constant velocity $40m/s$ . After what time will both cars meet each other?

Answer 1

Hint : to solve this question we have to know about acceleration, velocity, initial velocity, final velocity and all. We know that the terms velocity and speed give us an idea of how fast or slow an object is moving. Quite often, we come across situations where we need to identify which of the two or more objects is moving faster. One can easily tell the faster of the two if they are moving in the same direction on the same road. However, if their direction of motion is in the opposite direction, then it is difficult to determine the fastest.

Complete Step By Step Answer:
let us consider the distance covered by A be ${S_1}$
And the distance covered by B be ${S_2}$
B will catch A when ${S_2} = {S_1}$
We know that,
$S = ut + \dfrac{1}{2}a{t^2}$
Now putting the value we will get,
$40t + (\dfrac{1}{2} \times 0 \times {t^2}) = 0t + \dfrac{1}{2} \times 2 \times {t^2}$
40t = {t^2} \\\ t = 40 \\\
So, the right answer will be $40$ sec.

Note :
We know that, Acceleration is a vector quantity as it has both magnitude and direction. It is also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time. We can say, initial velocity describes how fast an object travels when gravity first applies force on the object. On the other hand, the final velocity is a vector quantity that measures the speed and direction of a moving body after it has reached its maximum acceleration.