A car of mass 1000 kg is moving with an initial velocity of 5 metre per second changes its velocity to 25 metre per second in 10 seconds. calculate ..
a, The initial velocity of the car
b, the final momentum of the car
c, the change of momentum of the car
d, the rate of change of momentum of the car
e, the force supplied by the the engine of the car.
Answers
Explanation:
We have,
Mass of the car, m = 1000 kg
Initial velocity of the car, u = 5 m/s
Final velocity of the car, v = 25 m/s
Time taken by the car, t = 10 s
Therefore,
a.) Initial velocity of the car,
b.) Final momentum of the car,
c.) Change in momentum of the car,
d.) The rate of change in the momentum of the car,
e.) Force applied by the the engine of the car,
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Given :-
- Mass of car = 1000 kg
- Initial velocity of the car = 5m/s
- Final velocity = 25m/s
- Time taken to change velocity = 10s
We need to find :-
- a) Initial velocity
- b) Final momentum
- c) Change in momentum
- d) Rate of change in momentum
- e) Force by the engine of the car
• Solution ( a ) :-
Initial velocity = ?
However by the given information ,
Given that initial Velocity = 5m/s
Hence , initial velocity = 5m/s
• Solution ( b ) :-
Final momentum ( pf ) = ?
As we know that ,
Final momentum ( pf ) = m × v
Substituting ,
• m = 1000 kg
• v = 25m/s
⇒ pf = 1000 × 25
⇒ Final momentum ( pf ) = 25000 kgm/s
• Solution ( c ) :-
Change in momentum ( ∆p ) = ?
As we know that ,
Change in momentum = Final momentum - initial momentum
• ∆p = pբ - p¡
Substituting ,
• Momentum = m × v
⇒ ∆p = 1000 × 25 - 1000 × 5
⇒ ∆p = 25000 - 5000
⇒ Change in momentum = 20000 kgm/s
• Solution ( d ) :-
Rate of change in momentum = ?
As we know that ,
Rate of change in momentum = pf - p¡/t
Simplifying the given formula ,
• Rate of change in momentum = mvf - mv¡/t
• Rate of change in momentum = m(v - u)/t
Here , ( v - u ) = change in momentum ( ∆p )
• Rate of change in momentum = m∆p/t
So , rate of change in momentum = m∆p/t
⇒ Rate of change in momentum = 100(20000)/10
⇒ Rate of change in momentum = 20 × 10⁴ kgm/s
• Solution ( e ) :-
Force = ?
As we know that ,
Force = m × a
So , here firstly we need to find acceleration .
a = v - u / t
⇒ a = 25 - 5/10
⇒ a = 20/10
⇒ Acceleration = 2 m/s²
Now , finding force
⇒ F = 1000 × 2
⇒ Force = 2000 N