Question

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

Answer 1

Given :-

Initial velocity = 18 km/h

Final velocity = 36 km/h

Time taken = 5 sec

To Find :-

The acceleration of the car.

The distance covered by the car in that time.​

Analysis :-

Here, we are given with initial velocity, final velocity and the time taken.

Using the first equation of motion you can easily substitute the given values and find the acceleration.

By the third equation of motion, find the distance accordingly.

Solution :-

We know that,

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

Using the formula,

$\underline{\boxed{\sf First \ equation \ of \ motion=v=u+at}}$

Given that,

Initial velocity (u) = 18 km/h = 5 m/s

Final velocity (v) = 36 km/h = 10 m/s

Time taken (t) = 5 sec

Substituting their values,

10 = 5 + (a) 5

10 - 5 = 5a

5a = 5

a = 5/5

a = 1 m/s

Therefore, the acceleration is 1 m/s.

Using the formula,

$\underline{\boxed{\sf Third \ equation \ of \ motion=v^2-u^2=2as}}$

Given that,

Initial velocity (u) = 18 km/h = 5 m/s

Final velocity (v) = 36 km/h = 10 m/s

Acceleration (a) = 1 m/s

Substituting their values,

(10)² - (5)² = 2 × 1 (s)

100 - 25 = 2s

2s = 75

s = 75/2

s = 37.5 m

Therefore, the distance covered by the car is 37.5 m.

Answer 2

Answer:

Given :-

• A car accelerats uniformly from 18 km/h to 36 km/h in 5 seconds.

To Find :-

1. What is the acceleration.
2. How much distance covered by the car.

Formula Used :-

❶ To find acceleration,

$\boxed{\bold{\large{v\: =\: u\: +\: at}}}$

❷ To find the distance covered by the car,

$\boxed{\bold{\large{{v}^{2} - {u}^{2} = 2as}}}$

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time taken
• s = Distance covered

Solution :-

❶ Given :

• v = 36 km/h = 10 m/s
• u = 18 km/h = 5 m/s
• t = 5 seconds

According to the question by using the formula we get,

❖ v = u + at

⇒ 10 = 5 + (a)(5)

⇒ 10 = 5 + 5a

⇒ - 5a = 5 - 10

⇒ - 5a = - 5

⇒ a = $\sf\dfrac{\cancel{- 5}}{\cancel{- 5}}$

➠ a = 1 m/s

$\therefore$ Acceleration (a) of a car is 1 m/s .

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❷ Now we have to find distance covered by a car,

From the above equation, we get the value of acceleration (a) = 1 m/s

❖ v² - u² = 2as

⇒ (10)² - (5)² = 2(1)(s)

⇒ 100 - 25 = 2s

⇒ 75 = 2s

⇒ - 2s = - 75

⇒ s = $\sf\dfrac{\cancel{- 75}}{\cancel{- 2}}$

➠ s = 37.5 m

$\therefore$ Distance covered by a car is 37.5 m .