Question

a body having uniform acceleration of 10 m/s^2 has a velocity of 100 m/s.in what time, the velocity will be doubled?​

Answer 1

Explanation:

A=10m/s^2

V=100m/s

therefore,v-u/t=a

10m/s^2=100m/s-0m/s /10s

Answer 2

Given :

• Acceleration of the body (a) = 10 m/s²
• Initial velocity of the body (u) = 100 m/s
• Final velocity of the body (v) = 200 m/s

To find :

• The time in which the velocity will be doubled

Solution :

Here, we are given the acceleration, initial velocity and the final velocity and we need to calculate the time. So, for that we will use equations of motion. There are two methods to calculate the time which are mentioned as follows :-

First method :

Using the first equation of motion,

• v = u + at

where,

• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration
• t denotes the time

Substituting the given values :-

⇒ 200 = 100 + (10)(t)

⇒ 200 = 100 + 10t

⇒ 200 - 100 = 10t

⇒ 100 = 10t

⇒ 100/10 = t

⇒ 10 = t

Therefore, the time time in which the velocity will be doubled = 10 seconds

Second method :

Firstly, we will calculate the distance travelled.

Using third equation of motion,

• v² - u² = 2as

where,

• s denotes the distance travelled
• v denotes the the final velocity
• u denotes the initial velocity
• a denotes the acceleration

Substituting the given values :

⇒ (200)² - (100)² = 2(10)(s)

⇒ (200 - 100)(200 + 100) = 20 × s

⇒ 100 × 300 = 20 × s

⇒ 30,000 = 20 × s

⇒ 30,000/20 = s

⇒ 3,000/2 = s

⇒ 1500 = s

The distance travelled by the object = 1500 m

Now, we will use the second equation of motion to calculate the time.

• s = ut + ½ at²

Substituting the given values :

⇒ 1500 = (100)(t) + ½ (10)(t)²

⇒ 1500 = 100t + ½ × 10 × t²

⇒ 1500 = 100t + 5t²

⇒ 5t² + 100t - 1500 = 0

⇒ 5(t² + 20t - 300) = 0

⇒ t² + 20t - 300 = 0

⇒ t² + 30t - 10t - 300 = 0

⇒ t(t + 30) - 10(t + 30) = 0

⇒ (t - 10)(t + 30) = 0

⇒ (t - 10) = 0 or (t + 30) = 0

⇒ t = 10 or t = - 30

Here, the value of t = - 30 will get rejected. Because time can never be negative.

So, the value of t = 10

Therefore, the time in which the velocity will be doubled = 10 seconds