Question

9. For how long should a force of 100 N act on a body of mass 20 kg so that it acquires a velocity of 100 ms ^ -1? [ans. 20 s]​

Answer 1

Hey mate this can help you.

Solution:-

Given:-

• Force (F) = 100N
• Mass of the body ( m) = 20 kg
• Final Velocity = 100 m / s

To Find:-

• Time .

Formula:-

• F = m × a ( where m is mass and a is acceleration.)
• v = u + a × t (where v is final velocity , a is acceleration , u is intital velocity and t is time.)

By the Problem:-

© Acceleration:-

$i) \: \: F = m × a \\ = > 100 = 20 \times a \\ = > 20a = 100 \\ = > a = \frac{100}{20} \\ = > a = 5 \: m/ {s}^{2}$

ii) Now, Initial Velocity = 0 m / s

Final velocity = 100 m / s

Acceleration (a) = $5 m / {s}^{2}$

© Time :-

$v = u + at \\ 100 = 0 + 5 \times t \\ = > 5t = 100 \\ = > t = \frac{100}{5} \\ = > t = 20 \: seconds$

®Answer:-

Time = 20 seconds.

Answer 2

Given :-

Force of the body = 100 N

Mass of the body = 20 kg

Final velocity of the body = 100 m/s

To Find :-

Time that should act on the body.

Analysis :-

Here we are given with the force, mass and the final velocity of the body.

Firstly, to find the acceleration substitute the values in the question such that force is equal to mass multiplied by acceleration.

Then use the first equation of motion to find the time taken.

Solution :-

We know that,

• f = Force
• a = Acceleration
• u = Initial velocity
• m = Mass
• v = Final velocity
• t = Time

Using the formula,

$\underline{\boxed{\sf Force=Mass \times Acceleration}}$

Given that,

Mass (m) = 20 kg

Force (f) = 100 N

Substituting their values,

⇒ f = ma

⇒ 100 = 20 × a

⇒ a = f/m

⇒ a = 100/20

⇒ a = 5 m/s

Using the formula,

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

Given that,

Final velocity (v) = 100 m/s

Initial velocity (u) = 0 m/s

Acceleration (a) = 5 m/s

Substituting their values,

⇒ 100 = 0 + 5 × t

⇒ 100 = 5 × t

⇒ t = 100/5

⇒ t = 20 sec

Therefore, force of 100 N should act 20 sec on a body.