Question

7. A car is travelling at 20 km/h, it speeds up to 60 km/h in 6 seconds. What is its
acceleration?
​

Answer 1

Answer:

1.85m/s^2

Explanation:

Given :

• Initial velocity,u = 20km/h = 20*1000/1*60*60 => 5.55m/s
• Final velocity,v = 60km/h =  => 16.66....m/s
• Time,t => 6 seconds

To Find :

• Acceleration = ?

Solution :

We know that :-

v = u+ at

Put their values and solve it

$\rightarrow \sf{16.66= 5.55+ a\times 6}$

$\rightarrow \sf{16.66-5.55=6a}$

$\rightarrow \sf{11.11 =6a}$

$\rightarrow \sf{\dfrac{11.11}{6} = a}$

$\rightarrow \sf{a=1.85m/s^2}$

Therefore,car will accelerate 1.85m/s^2

Answer 2

Answer : -

Given : -

A car is travelling at 20 km/hr , it speeds up to 60 km/hr in 6 seconds .

Required to find : -

• Acceleration ?

Formula used : -

$\boxed{\tt{\bf{ a = \dfrac{ v - u }{ t } }}}$

Here,

• a = acceleration

• v = Final velocity

• u = Initial velocity

• t = time taken

Solution : -

A car is travelling at 20 km/hr , it speeds up to 60 km/hr in 6 seconds .

we need to find the acceleration of the car .

From the given data we can conclude that ;

• Initial velocity of the car ( u ) = 20 km/hr

• Final velocity of the car ( v ) = 60 km/hr

• Time taken ( t ) = 6 seconds

Here,

we need to convert the initial & final velocity from km/hr into m/s .

Using the formula ,

$\sf{1 \; km/hr = \dfrac{5}{18} m/s }$

20 km/hr = ? m/s

=> 20 x 5/18

=> 10 x 5/9

=> 50/9

Similarly,

60 km/hr = ? m/s

=> 60 x 5/18

=> 10 x 5/3

=> 50/3

Hence,

• Initial velocity of the car ( u ) = 50/9 m/s

• Final velocity of the car ( v ) = 50/3 m/s

Using the formula ;

$\boxed{\tt{\bf{ a = \dfrac{ v - u }{ t } }}}$

$\sf a = \dfrac{ \dfrac{50}{3} - \dfrac{50}{9} }{6} \\ \\ \sf a = \dfrac{ \dfrac{150}{9} - \dfrac{50}{9} }{6} \\ \\ \sf a = \dfrac{ \dfrac{150 - 50}{9} }{6} \\ \\ \sf a = \dfrac{ \dfrac{100}{9} }{6} \\ \\ \sf a = \frac{100}{9} \times \frac{1}{6} \\ \\ \sf a = \frac{100}{54} \\ \\ \sf a = 1.8518 \dots \dots \: \\ \\ \sf a = 1.85 \: m {s}^{ - 2} ( approximately )$

Therefore,

Acceleration of the car = 1.85 m/s² ( approximately )

Additional Information : -

The Equations of motion are ;

• v = u + at

• s = ut + ½ at²

• v² - u² = 2as

Here,

v = Final velocity

u = Initial velocity

a = acceleration

s = displacement

t = time taken

The 1st equation of motion gives us the relationship between the final velocity and time .

The 2nd equation of motion gives us the relationship between the displacement and time

The 3rd equation of motion gives us the relationship between the final velocity and displacement .

Knowing these relationships helps us to know where we can use these equations correctly .

These equations of motion are only applicable when the acceleration is constant .

The SI unit of acceleration is m/s² .

That is why we need to convert the final velocity and initial velocity from km/hr to m/s.