Question

A car moving with a velocity of 10 m/s accelerates uniformly at 1
m/s^2 until it reaches a velocity of 15 m/s.Calculate (i) the time taken (ii) the distance travelled during the acceleration.
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Answer 1

Explanation:

Given:-

• Initial velocity (u) = 10m/s

• Final velocity (v) = 15m/s

• Acceleration (a) = 1m/s²

To Find:-

• The time taken by the car.

• The distance travelled by the car.

Solution:-

u = 10m/s , v = 15m/s , a = 1m/s²

Time (t) = ?

Distance (s) = ?

Using 1st equation of motion:-

$\sf \implies v = u + at$

$\sf \implies 15 = 10 + 1(t)$

$\sf \implies 10 + t = 15$

$\sf \implies t = 15 - 10$

$\sf \implies t = 5s$

$\sf \therefore \underline{\:\: \underline{\: Time \: taken = 5s\:}\:\:}$

Using 3rd equation of motion:-

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

$\sf \implies s = (10 \times 5) + \dfrac{1}{2} \times 1 \times {(5)}^{2}$

$\sf \implies s = (50) + \dfrac{1}{2} \times 25$

$\sf \implies s = (50) + 12.5$

$\sf \implies s = 62.5$

$\sf \therefore \underline{\:\: \underline{\: Distance\: travelled= 62.5m\:}\:\:}$

Answer 2

Answer:

Given :-

• A car moving with a velocity of 10 m/s accelerates uniformly at 1 m/s² until it reaches a velocity of 15 m/s.

To Find :-

1. How much time taken by the car.
2. What is the distance travelled during the acceleration.

Formula Used :-

❶ To find time we have to use the formula of 1st equation of motion,

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

where,

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

❷ To find distance we have to use the formula of 3rd equation of motion,

$\boxed{\bold{\large{s\: =\: ut\: +\: \dfrac{1}{2}a{t}^{2}}}}$

where,

• s = Distance travelled
• u = Initial velocity
• t = Time
• a = Acceleration

Solution :-

Given :

• Initial velocity (u) = 10 m/s
• Final velocity (v) = 15 m/s
• Acceleration (a) = 1 m/s²

❶ First, we have to find the time,

⇒ 15 = 10 + 1 × t

⇒ 15 = 10 + t

⇒ 10 + t = 15

⇒ t = 15 - 10

➠ t = 5 seconds

$\therefore$ Time taken by a car is 5 seconds .

❷ Now, we have to find the distance travelled by a car,

⇒ s = (10)(5) + $\dfrac{1}{2}$ × 1(5)²

⇒ s = 50 + $\dfrac{1}{2}$ × 25

⇒ s = 50 + 12.5

➠ s = 62.5 m

$\therefore$ Distance travelled during the acceleration is 62.5 m .