Question

A car travels from stop A to stop B with a speed of 30 km/h and then returns back to A with a speed of 50 km/h. Find
(i) displacement of the car. (ii) distance travelled by the car. (iii) average speed of the car.

Answer 1

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

(i) Displacement of the car = 0 m/s.

(ii) Total distance travelled = 2x km.

(iii) Average speed = 37.5 km/hr.

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

• A car travels from stop A to stop B with a speed of 30km/hr.
• It travels back from stop B to stop A with a speed of 50km/hr.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• Displacement of the car.
• Distance travelled by the car.
• Average speed of the car.

${\rm{\purple{\underline{\underline{Formula \: Used: }}}}}$

$\rm \: t = \frac{s}{v}$

where,

t = time taken by the car while going A to B

s = distance travelled by the car

v = speed by which the car is moving

$\rm \: Average \: speed = \frac{total \: distance}{total \: time \: taken}$

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

(1) Displacement is the shortest distance travelled by an object. Here, the car travels from A to B and returns to stop A means it came back to the point from where it started.

Thus, the Displacement of the car is 0 m/s

__________________________________

(2) Let the distance travelled by the car from stop A to stop B = x km

The car travels A to B and returns back to B.

Thus, total distance travelled = 2x km

__________________________________

(3) Time while going from A to B = $\rm \: \frac{distance \: travelled}{speed}$

$\rm \longrightarrow \: \frac{x}{30} hours$

Time while returning from B to A = $\rm \: \frac{distance \: travelled}{speed}$

$\rm \longrightarrow \: \frac{x}{50} hours$

Total Time taken :-

$\rm \longrightarrow \: \frac{x}{50} + \frac{x}{30}$

$\rm \longrightarrow \: \frac{3x + 5x}{150}$

$\rm \longrightarrow \: \frac{ \cancel8x}{ \cancel{150}}$

$\rm \longrightarrow \: \frac{4x}{75} hrs$

$\rm \: Average \: speed = \frac{total \: distance}{total \: time \: taken}$

substituting the values,

$\rm \: Average \: speed = \frac{2x}{ \frac{4x}{75} }$

$\rm \: Average \: speed = \frac{2x \times 75}{4x}$

$\rm \: Average \: speed = \frac{ \cancel{2x} \times 75}{ \cancel{4x}}$

$\rm \: Average \: speed = \frac{75}{2}$

$\rm \: Average \: speed = \pink{ 37.5 \: km/ hr}$

Hence,

(1) Displacement of the car is 0 m/s.

(2) Total distance travelled is 2x km.

(3) Average speed is 37.5 km/hr.