Question

A car accelerates from rest to a speed of 36 km/h in 20 seconds. What is the acceleration of the car in m/s2?

Answer 1

Given:

Initial velocity of car,u= 0 km/h

(Since, it starts from rest)

Final velocity of car,v= 36 km/h

Time taken by car,t= 20 s

To Find:

Acceleration of car in m/s²

Solution:

We know that,  

• According to first equation of motion for constant acceleration,

$\purple{\underline{\boxed{\bf{v=u+at}}}}$

where,

v is final velocity

u is initial velocity

a is acceleration

t is time taken

━━━━━━━━━━━━━━━━━━━━━━━━━━

It is given that,

$\longrightarrow\rm{u=0\ km/h=0\times\dfrac{5}{18}\ m/s=0\ m/s}$

$\longrightarrow\rm{v=36\ km/h=36\times\dfrac{5}{18}\ m/s=10\ m/s}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

Let the acceleration of car be 'a'

So, on applying first equation of motion on car, we get

$\longrightarrow\rm{v=u+at}$

$\longrightarrow\rm{10=0+a(20)}$

$\longrightarrow\rm{10=20a}$

$\longrightarrow\rm{20a=10}$

$\longrightarrow\rm{a=\dfrac{10}{20}}$

$\longrightarrow\rm\green{a=0.5\ m/s^{2}}$

Hence, acceleration of car is 0.5 m/s².

Answer 2

$\Huge\sf\red{★AnsweR:}$

Let’s review the 4 fundamental kinematic equations of motion for constant acceleration (strongly recommend you commit these to memory – they will serve you well) :

$<font color=pink>$

s = ut + ½at^2 …. (1)

v^2 = u^2 + 2as …. (2)

v = u + at …. (3)

s = (u + v)t/2 …. (4)

$<font color=black>$

where s is distance, u is initial velocity, v is final velocity, a is acceleration and t is time.

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In this case, we know u = 0, v = 36km/h = 10m/s, t = 18s and we want to find a, so we use equation (3)

$<font color=blue>$

v = u + at

10 = 0 + 18a

a = 10/18 = 0.556

$<font color=green>$

The acceleration is 0.56m/s^2