A motor car of mass 1200kg is moving along a straight line with a uniform velocity of 90km/h.itsmvelocity is slowed down to 18km/h in 4 s by an unbalanced external force.calculate th acceleration and change in momentum of the car . Also calculate the magnitude of force required.
Here, m = 1200 kg, m = 90 km/h = 90*1000 m60*60 s25 m's
v = 18 km/h = 18*1000 m60*60 s= 5m/s,t = 4s
Alcceleration,a =v-ut = 5-254=5 m/s^2
Change in momentum = m (v - u) = 1200 (5 -25) = -24000 kg m's
Force required, F = ma = 1200 (-5) = -6000 N
Magnitude of force required = 6000 N
Negative sign shows that force is opposing the motion.
Acceleration =V2 _ v1 / t =5m/s2
F=ma =12oo×5 =6000
F= rate of change of momentum
F= momentum /time
Momentum =6000× 4= 24000
To calculate the acceleration of the car, we need to use the formula:
Acceleration (a) = (Final velocity - Initial velocity) / Time
In this case, the initial velocity is 90 km/h (which needs to be converted to m/s), the final velocity is 18 km/h (also needs to be converted to m/s), and the time is 4 seconds.
Converting km/h to m/s:
90 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 25 m/s (approx.)
18 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 5 m/s (approx.)
Using the formula:
Acceleration (a) = (5 m/s - 25 m/s) / 4 s = -5 m/s²
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, meaning the car is slowing down.
To calculate the change in momentum of the car, we use the formula:
Change in momentum = Mass * (Final velocity - Initial velocity)
The mass of the car is given as 1200 kg, the initial velocity is 25 m/s, and the final velocity is 5 m/s.
Change in momentum = 1200 kg * (5 m/s - 25 m/s) = -24,000 kg·m/s
Again, the negative sign indicates that the change in momentum is in the opposite direction to the initial momentum, meaning it is decreasing.
Finally, to calculate the magnitude of the force required, we use Newton's second law of motion:
Force (F) = Mass * Acceleration
In this case, the mass is still 1200 kg and the acceleration is -5 m/s².
Force (F) = 1200 kg * (-5 m/s²) = -6000 N (approx.)
Once again, the negative sign is there to indicate that the force is in the opposite direction to the motion of the car, acting against it.
So, the acceleration of the car is -5 m/s², the change in momentum is -24,000 kg·m/s, and the magnitude of the force required is 6000 N.