Question

Example 8.6 A car accelerates uniformly from 18 km h to 36 km h in 5 s. Calculate (i) the acceleration and (ii) the distance covered by the car in that time.​

Answer 1

Answer:

A)

Given parameters

Time taken (t) = 5 sec

Initial velocity (u) =18 km/hour

u=18×100060×60s

 u = 5 m/s

Final velocity (v) =36km/hour

v=36×100060×60s

v =10 m/s

Acceleration a = v-u / t

a = 10 - 5 / 5

a = 1m/s2

B)

Distance travelled S = u t + (1/2) a × t2

S= 5 × 5 + (1/2) × 1 × $5^{2}$

S = 25 + (1/2) × 25

S = 25 + 12.5

S = 37.5 m

Hence

acceleration a =1 m/s2

Distance travelled  S =37.5 m

Answer 2

$\purple{\bf\huge{ \underline{\underline{Question : }}}}$

A car accelerates uniformly from 18 km h to 36 km h in 5 s. Calculate

(i) the acceleration and

(ii) the distance covered by the car in that time.

$\purple{\bf\huge{ \underline{\underline{Answer : }}}}$

$\bf 1. \: Acceleration = 1\:m {s}^{ - 2}$

$\bf 2. \:Distance \: covered = 37.5\:m$

$\purple{\bf\huge{ \underline{\underline{Explanation : }}}}$

$\bf Given\begin{cases} \sf Initial\: Velocity(u) = 18 \: km \: {h}^{ - 1} \\ \\ \sf Final \: Velocity(v) = 36\: km \: {h}^{ - 1} \\ \\ \sf Time(t) =5 \: s \end{cases}$

$\longmapsto\sf u = 18 \: km \: {h}^{ - 1} \\ \longmapsto\sf u =5 \: m \: {s}^{ - 1} \: \: \: \: \:$

$\longmapsto \sf v = 36 \: km \: {h}^{ - 1} \\ \longmapsto\sf v=10 \: m \: {s}^{ - 1} \: \:$

$\red{ \bf \underline{Acceleration : }}$

$\bf Using \: formula :$

$\longmapsto\boxed{ \bf v = u + at}$

$\longmapsto \bf 10 = 5 + a(5) \\ \\ \longmapsto \bf5 + 5a = 10 \: \: \: \\ \\ \longmapsto \bf5a = 10 - 5 \: \: \: \\ \\ \longmapsto \bf5a = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longmapsto \bf a = \frac{5}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \longmapsto \bf a =1 \: m \: {s}^{ - 2} \: \: \:$

$\red{ \bf \underline{ Distance \: Covered : }}$

$\bf Using \: formula :$

$\longmapsto\boxed{ \bf {v}^{2} - {u}^{2} = 2as}$

$\bf \longmapsto ({10})^{2} - ({5})^{2} = 2(1)s \\ \\ \bf \longmapsto100 - 25 = 2s \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \longmapsto2s = 100 - 25 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \longmapsto2s = 75 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \longmapsto s = \frac{75}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf \longmapsto s = 37.5 \: m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$