Question

A car P moves due east with a speed of $10m/s$ and another car Q moves due west with a speed$15m/s$. Then, how can we find the distance moved by the car Q during the time interval in which they completely cross each other? (At the moment$t = 0$, the separation between the cars is $90m$ and the length of each car is$5m$.)
$(A)60m$
$(B)15m$
$(C)330m$
$(D)54m$

Answer 1

Hint : The speed of both cars is given, using those values we will find the relative velocity of the car. After that, we can find the total distance covered by the car with the help of the length of each car and the separation between the cars. By using these values, we will find the distance traveled by car during the time interval in which they completely cross each other.

Formula used:
$velocity\left( v \right) = \dfrac{{displacement\left( d \right)}}{{time\left( t \right)}}$

Complete step-by-step solution:
Given that, speed of car P and Q is ${v_p} = 10m/s,{v_q} = 15m/s$
Length of each car $= 5m$and separation between the cars$= 90m$
Total distance covered$\left( d \right) = 90 + 5 + 5 = 100m$
Relative velocity$\left( v \right) = 10 + 15 = 25m/s$
Time taken$\left( t \right) = \dfrac{d}{v} = \dfrac{{100}}{{25}} = 4s$
Distance traveled by Q,$\left( {{d_p}} \right) = {v_p} \times t = 15 \times 4 = 60m$
Hence, the distance moved by the car Q during the time interval in which they completely cross each other is$60m$.
So, option A is correct.

Note: Speed is that the distance traveled by an object in unit time. Speed may be a scalar quantity. This suggests it has no specified direction. Speed refers to how briskly an object is moving, or essentially the rate at which the distance is covered. Velocity may be a physical vector quantity. It has a magnitude moreover as direction. In calculus, velocity is the first derivative of the position with respect to time. Velocity, in other words, is the rate of change within the position of the body with relevance to time. Its SI unit is a meter per second. Relative velocity is fundamental in both classical and physical physics. Relative velocity may be a measurement of velocity between two objects as calculated in a single coordinate system.