Answer

Verified

405k+ views

**Hint:**Work done by the force is equal to change in kinetic energy of the body. Use the relation between work done and applied force. Also, take the final velocity of the car as zero.

**Formula used:**

\[\dfrac{1}{2}mv_f^2 - \dfrac{1}{2}mv_i^2 = Fd\]

Here, \[{v_f}\] is the final velocity of the car and \[{v_i}\] is the initial velocity of the car, F is the braking force and d is the distance.

**Complete step by step answer:**

We know the relation between force and work done. The work done is the product of force and displacement of the body.

Therefore,

\[W = Fd\] …… (1)

Here, F is the braking force and d is the distance travelled by the car after applying the brakes.

Also, the work done is the change in the kinetic energy of the object. Therefore, we can write,

\[\dfrac{1}{2}mv_f^2 - \dfrac{1}{2}mv_i^2 = W\] …… (2)

Here, \[{v_f}\] is the final velocity of the car and \[{v_i}\] is the initial velocity of the car.

Equate equations (1) and (2).

\[\dfrac{1}{2}mv_f^2 - \dfrac{1}{2}mv_i^2 = Fd\]

Since the force is applied due to the brakes, the direction of the force is in the opposite direction of the motion of the car. Therefore, the above equation becomes,

\[\dfrac{1}{2}mv_f^2 - \dfrac{1}{2}mv_i^2 = - Fd\]

Since the final velocity of the car is zero, the above equation becomes,

\[\dfrac{1}{2}mv_i^2 = Fd\] …… (3)

For the car moving with velocity 60 km/h, we can write the above equation as follows,

\[\dfrac{1}{2}mV_i^2 = Fd'\] …… (4)

Divide equation (2) by equation (1).

\[\dfrac{{\dfrac{1}{2}mV_i^2}}{{\dfrac{1}{2}mv_i^2}} = \dfrac{{Fd'}}{{Fd}}\]

\[ \Rightarrow \dfrac{{V_i^2}}{{v_i^2}} = \dfrac{{d'}}{d}\]

\[\therefore d' = {\left( {\dfrac{{{V_i}}}{{{v_i}}}} \right)^2}d\]

Substitute 60 km/h for \[{V_i}\], 30 km/h for \[{v_i}\] and 8 m for d in the above equation.

\[d' = {\left( {\dfrac{{60\,km/h}}{{30\,km/h}}} \right)^2}\left( {8\,m} \right)\]

\[ \Rightarrow d' = 4 \times \left( {8\,m} \right)\]

\[\therefore d' = 32\,m\]

**So, the correct answer is “Option D”.**

**Note:**

Since the braking force is the same in both the cases, you can also solve this question using kinematic relation \[{v^2} = {u^2} + 2as\]. Substitute 0 for final velocity of the car for both the cases and rearrange

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Who founded the Nalanda University 1 Mauryan 2 Guptas class 6 social science CBSE