Question

A car drives north for $35$ minutes at $85\,kmh{r^{ - 1}}$ and then stops for $15\min .$ The car continues north travelling $130\,km$ in $2$ hours. What is the total displacement and average velocity?

Answer 1

In order to solve this question, we should know that displacement covered by the body is distance between final and initial point of path followed by the body and average velocity is the ratio of net displacement and total time taken by the body to cover that displacement, here we will use given information to find displacement and average velocity of the car.

Complete step by step answer:
According to the question, we have given that car travels in one direction north and let ${d_1}$ be the distance covered by car in $t = 35\min = \dfrac{7}{{12}}hr$ with a velocity of $v = 85\,kmh{r^{ - 1}}$ so, using distance formula we get,
${d_1} = v \times t$
On putting value of parameters we get,
${d_1} = 85 \times \dfrac{7}{{12}}$
$\Rightarrow {d_1} = 49.6km$

Now, a car stops for $t = 15\min$ in which it covers zero distance and then, car covers a distance of ${d_2} = 130km$ for time period of $t = 2hr$ so, Net displacement covered by the car D is,
$D = {d_1} + {d_2}$
On putting the value of parameters we get,
$D = 130 + 49.6$
$\Rightarrow D = 179.6\,km$

For average velocity we have, net displacement by car is $D = 179.6\,km$ and total time taken by the car T is
$T = \dfrac{7}{{12}}hr + 2hr + 15\min$
Or we can write it as,
$T = 0.58 + 2 + 0.25 = 2.83hr$
And average velocity $V$ is,
$\Rightarrow V = \dfrac{D}{T}$
On putting the value of parameters we get,
$V = \dfrac{{179.6}}{{2.83}} \\\ \therefore V= 63.46\,kmh{r^{ - 1}}$

Hence, the displacement covered by the car is $179.6\,km$ and the average velocity of the car is $63.46\,kmh{r^{ - 1}}$.

Note: It should be remembered that, basic conversion of time from minutes into hour is used here as $1\min = \dfrac{1}{{60}}hr$ and car covers the distance in one direction only so here, displacement and distance have the same magnitude but displacement is a vector quantity and here the direction of displacement is in North.