Question

16, A car accelerates by 50 m/s². It would attain a speed
of 100 km/h from rest, in
(a) 0.56 s (b) 0.28 s (c) 2 s (d) 1.12
0.0.28
ne hour​

Answer 1

Given

A car accelerates by 50 m/s². It would attain a speed  of 100 km/h from rest, in

To Find

It would attain a speed  of 100 km/h from rest, in

• (a) 0.56 s
• (b) 0.28 s
• (c) 2 s
• (d) 1.12  s

Solution

We know that

Equation of motion

$\sf \longrightarrow v=u+at$

Here

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

Units

• v = metre/second (m/s)
• u = metre/second (m/s)
• a = metre/ square second (m/s²)
• t = second (s)

According to the question

We are asked to find the time it would attain a speed  of 100 km/h from rest

Hence

We must find "t"

Therefore

$\sf \longrightarrow t=\dfrac{v-u}{a}$

Given that

A car accelerates by 50 m/s². It would attain a speed  of 100 km/h from rest, in

[1 km/h = 0.2778 m/s]

Hence

• u = 0 m/s [starts from rest]
• v = 100 km/h = 27.78 m/s
• a = 50 m/s²

Substituting the values

We get

$\sf \longrightarrow t=\dfrac{27.78-0}{50} \ s$

$\sf \longrightarrow t=\dfrac{27.78}{50} \ s$

Therefore

$\sf \longrightarrow t=0.56 \ s$

Hence

Option (a) is correct

Answer 2

Given:-

• acceleration = 50m/s²
• initial velocity (u) = 0m/s
• final velocity (v) = 100km/h

Conversion of 100km/hr. into m/s.

$\sf\dfrac{100}{1}$ × $\sf\dfrac{5}{18}$ = $\dfrac{250}{9}$ m/s.

To find:-

• time period to attain this speed.

Formula to be used:-

$\implies$ $\huge \underline{\boxed{\sf v = u+at}}$

Solution:-

$\implies$ $\sf\dfrac{250}{9}$ = 0 + 50×t

$\implies$ $\sf\dfrac{250}{9}$ × $\sf\dfrac{1}{50}$ = t

$\implies$ t = $\sf\dfrac{5}{9}$ = 0.555... sec.

$\implies$ 0.56sec.

hence, ur option is a.