Question

a truck sterling from rest maintain a constant acceleration of 10m/s 2. how long will it take to cover 20km
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Answer 1

Given :

Initial velocity of the truck = zero

Accerlation of truck = 10m/s²

Distance covered = 20 km = 20,000m

To find :

The time taken to cover 20km

Solution :

As we are provided with initial velocity, accerlation and distance covered we can use second equation of kenimatics.

so, using second equation of kenimatics that is,

$\boxed{ \bf s = ut + \dfrac{1}{2} {at}^{2} }$

here,

• s denotes distance covered
• u denotes initial velocity
• t denotes time
• a denotes acceleration

by substituting all the given values in the equation,

$: \implies{ \sf s = ut + \dfrac{1}{2} {at}^{2} }$

$: \implies{ \sf 20000 = (0)t + \dfrac{1}{2} {(10)t}^{2} }$

$: \implies{ \sf 20000 = \dfrac{1}{2} \times 10 \times {t}^{2} }$

$: \implies{ \sf 20000 = 5\times {t}^{2} }$

$: \implies{ \sf {t}^{2} = \dfrac{20000}{5} }$

$: \implies{ \sf {t}^{2} = 4000}$

$: \implies{ \sf t = \sqrt{4000} }$

$: \implies \underline { \boxed{ \sf t = 63.2 \: sec}}$

thus, time taken to cover 20 km is 63.2sec.

Answer 2

Question :

A truck sterling from rest maintain a constant acceleration of 10m/s² . How long will it take to cover 20 km ?

Given that :

• Distance covered by a truck = 20 km = 20,000 metres. {Changing km into metres 1 km = 1000 metres ; hence, 20 × 1000 = 20,000 metres}.
• Constant acceleration = 10m/s²
• Initial velocity = 0 {Because the truck sterling at a rest that time that's why this become 0}.

To find :

• Time taken to cover 20 km means 20,000 metres.

Solution :

• Time taken to cover 20 km means 20,000 metres = 63.2 seconds

Using concept,

• $\sf Concept \begin{cases} & \sf{Distance \: covered \: formula} \end{cases}$

Using formula,

• $\sf Formula \begin{cases} & \sf{s = \bf{ut \: + \: \frac{1}{2}at^{2}}} \end{cases}$

We also write these as :

• Acceleration as a.
• Initial velocity as u.
• Time as t.
• Covered distance as s.

What does the question says ?

• This question says that there is a truck and it's sterling from maintaining a rest of 0 as its initial velocity and it's constant acceleration is 10m/s² and it cover a distance of 20 km means 20,000 metres. Afterthat it ask us to find the time to cover 20 km.

Let's see the procedure :

• It's cleared that what is given or what to find let see it again to understand the concept properly. Truck's initial velocity, distance and acceleration is given and we have to find the time taken by the truck in 20 kms. Now using the 2nd law of Kinematic equations we have to insert the values.

Full solution :

Putting the values according to this formula we get the following results.

$\sf{s \: = \: ut \: + \: \frac{1}{2}at^{2}}$

$\sf{20,000 \: = \: (0)t \: + \: \frac{1}{2}(10)t^{2}}$

$\sf{20,000 \: = \: \frac{1}{2} \: \times 10 \times t^{2}}$

$\sf{20,000 \: = 5 \times \: t^{2}}$

$\sf{t^{2} \: = \: \frac{20,000}{5}}$

$\sf{t^{2} \: = \: 4,000}$

$\sf{t \: = \: \sqrt{4000}}$

$\sf{t \: = \: 63.2 \: seconds}$

Hence, 63.2 seconds is the time taken to covered 20 km.