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

$\sf\underline{Given :-}$

• 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.

$\sf\underline{To\: Find :-}$

• What is the distance travelled by a body.

$\sf\underline{Formula \:Used :-}$

❶ To find acceleration we know that,

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

Where,

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

❷ To find distance travelled we know that,

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

where,

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

$\bf\underline{Solution :-}$

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,

• $\sf a =\: \dfrac{10}{0.5}$

• $\sf a =\: \dfrac{10 \times 10}{5}$

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

• $\sf\bold{\red{a =\: 20\: m{s}^{2}}}$

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,

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

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

• $\sf s =\: 0 + 10 \times$

• $\sf s =\: 0 + 1000$

• ➦ $\sf\bold{\purple{s =\: 1000\: m}}$

∴ The distance travelled by body is 1000 m .

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Answer 2

★ The distance travelled by the body is 1000 m (1 km).

Step-by-step explanation

Analysis -

We're provided with the information that a body of mass 500 g is at rest on a frictionless surface. In case 10 newtons of force is applied on it, the distance travelled by the body in 10 seconds has been asked to find.

Solution -

We know that there are three equations of motion, from which we can find any of the acceleration, velocity (initial/final), distance/displacement or time taken in a question. The three equations are as follows:

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boxed{\begin{array}{c} \sf \pmb{1) \: v = u + at \: \: \: \: \: \: \: } \\ \\ \sf \pmb{2) \: s = ut + \dfrac{1}{2}a {t}^{2} } \\ \\ \sf \pmb{3) \: {v}^{2} - {u}^{2} = 2as \: }\end{array}}\end{gathered}\end{gathered}$

Now, according to our question, we have the following values:

• Initial velocity (u) = 0 m/s
• Time (t) = 10 s
• Mass (m) = 0.5 kg (500 g)
• Force (F) = 10 N

As per the above values, we have to choose the second equation of motion since, 1st and 3rd equations require final velocity, which is an unknown criteria. And, the acceleration (a) in the second equation can be found by using the formula:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf \pmb{F = ma}}$

On substituting the values,

$\twoheadrightarrow{ \sf{F= ma}} \\ \\ \twoheadrightarrow{ \sf{10 =0.5(a) }} \\ \\ \twoheadrightarrow{ \sf{ \dfrac{10}{0.5} = a }} \\ \\ \twoheadrightarrow{ \sf{ \dfrac{10(10)}{5 } = a}} \\ \\ \twoheadrightarrow{ \sf{ \dfrac{ \cancel{100}}{ \cancel5} = a }} \\ \\ \twoheadrightarrow{ \underline{ \underline{ \sf \pmb{20 \: m /{s}^{2} = a}}}}$

We got the value of acceleration. So, let us plug in the value of 'a' and other requirements in the second equation and solve for 's'.

$\dashrightarrow{ \sf \pmb{s = ut + \dfrac{1}{2}a {t}^{2} }} \\ \\ \dashrightarrow{ \sf{s = 0 \times 10 + \dfrac{1}{2} \times 20 \times {(10)}^{2} }} \\ \\ \dashrightarrow{ \sf{s = 0 \times 10 + \dfrac{1}{2} \times 20 \times 100 }} \\ \\ \dashrightarrow{ \sf{s = 0 + \dfrac{1}{2} \times 20 \times 100}} \\ \\ \dashrightarrow{ \sf{s = 0 + \dfrac{1}{ \cancel2} \times \cancel{2000} }} \\ \\ \dashrightarrow{ \sf{s =0 + 1 \times 1000 }} \\ \\ \dashrightarrow{ \sf{s = 0 + 1000}} \\ \\ \dashrightarrow \underline{ \boxed{ \frak{\pmb{s = 1000 \: m}}}}$

And this is the required answer! Hence, the distance travelled by the body in 10 seconds is 1000 m, i.e., 1 km.

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