Question

A body of mass 500g is at rest on a frictionless surface. What is the distance
travelled by it in 10s when acted upon by a force of 10 N?

Answer 1

Given :-

Mass of the body = 500 g

Force acting on the body in 10 s = 10 N

To Find :-

The distance  travelled by it in 10s when acted upon by a force of 10 N.

Analysis :-

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

Then using the second equation of motion, substitute the values we got and find the displacement accordingly.

Solution :-

Using the formula,

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

We know that,

• f = Force
• m = Mass
• a = Acceleration

Given that,

Force (f) = 10 N

Mass (m) = 500 g = 0.5 kg

Substituting their values,

⇒ 10 = 0.5 × a

⇒ a = f/m

⇒ a = 10/0.5

⇒ a = 20 m/s²

Using the formula,

$\underline{\boxed{\sf Second \ equation \ of \ motion=s=ut+\dfrac{1}{2} at^2}}$

We know that,

• s = Displacement
• u = Initial velocity
• t = Time taken
• a = Acceleration

Given that,

Initial velocity (u) = 0 m/s

Time taken (t) = 10 sec

Acceleration (a) = 20 m/s²

Substituting their values,

⇒ s = 0 × 10 + (1/2) × 20 × 10²

⇒ s = (1/2) × 20 × 100

⇒ s = 10 × 100

⇒ s = 1000 m

Therefore, the distance  travelled by the body is 1000 m.

Answer 2

Answer:

Given :-

• A body of mass 500 g is at rest on a frictionless surface and it's in 10 s when acted upon by a force of 10 N.

To Find :-

• What is the distance travelled by a body.

Formula Used :-

❶ To find acceleration we know that,

${\purple{\boxed{\large{\bold{a =\: \dfrac{F}{m}}}}}}$

where,

• a = Acceleration
• F = Force
• m = Mass

❷ To find distance travelled we know that,

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

where,

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

Solution :-

❶ First, we have to find acceleration,

Given :

• Force (F) = 10 N
• Mass (m) = 500 g = $\sf\dfrac{500}{1000}$ = 0.5 kg

According to the question by using the formula we get,

⇒ $\sf a =\: \dfrac{10}{0.5}$

⇒ $\sf a =\: \dfrac{10 \times 10}{5}$

⇒ $\sf a =\: \dfrac{\cancel{100}}{\cancel{5}}$

➠ $\sf\bold{\green{a =\: 20\: m{s}^{2}}}$

Hence, the acceleration is 20 m/s² .

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

Given :

• Initial velocity (u) = 0 m/s
• Time (t) = 10 seconds
• Acceleration (a) = 20 m/s²

According to the question by using the formula we get,

↦ $\sf s =\: 0(10) + \dfrac{1}{2} \times 20 \times {(10)}^{2}$

↦ $\sf s =\: 0 + \dfrac{1}{\cancel{2}} \times {\cancel{20}} \times 100$

↦ $\sf s =\: 0 + 10 \times 100$

↦ $\sf s =\: 0 + 1000$

➦ $\sf\bold{\red{s =\: 1000\: m}}$

$\therefore$ The distance travelled by body is 1000 m .