What is the work to be done to increase the velocity of a car from 36 km/h 1 to 54 km/h 1 if the mass of the car is 2000 kg?

Solve the following example.
The velocity of a car increase from 54 km/hr to 72 km/hr. How much is the work done if the mass of the car is 1500 kg?

Here, v = 72 km/h = 20 m/s, u = 54 km/h = 15 m/s, m = 1500 kgWork done by the car = Change in kinetic energy of the cari.e. `W = K.E_f - K.E_i``W = 1/2 xx m xx v^2 - 1/2 xx m xx u^2 = 1/2 xx m(v^2 - u^2)`

= `1/2 xx 1500 (20^2 - 15^2)` = 131250 J

  Is there an error in this question or solution?

Text Solution

`156200J``156250J``156275J``156300J`

Answer : B

Solution : Mass of the car, `m =1500 kg`, <br> initial velocity of car, `u = 30 km h^(-1)` <br> `=(30xx1000 m)/((60 xx 60 s)` <br> `=25//3 ms^(-1)` <br> Similarly, the final velocity of the car, <br> `v = 60 km h^(-1)` <br> `=50//3 ms^(-1)` <br> Therefore, the initial kinetic energy of the car, <br> `E_(kt) = (1)/(2) m u^(2)` <br> `=(1)/(2)xx1500 kg xx (25//3 ms^(-1))^(2)` <br> = 156250/3 J <br> The final kinetic energy of the car, <br> `E_(kf)=(1)/(2) xx1500 kg xx(50//3 ms^(-1))^(2)` <br> = 625000/3 J. m <br> Thus, the work done = Change in kinetic energy <br> `=E_(kf) - E_(kt)` <br> = 156250 J.

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