From the information given, the bus and the car got stuck after the collision and moved towards north together. Let v represent the initial velocity at which both the bus and car were moving together after the collision. According to the law of conservation of momentum, momentum is conserved. This means that
Total initial momentum = total final momentum
This is expressed as
m1u1 + m2u2 = (m1 + m2)V
Since the car is moving in the opposite direction of the bus, the equation would be
m1u1 - m2u2 = (m1 + m2)
From the information given,
m1 = 3300
u1 = 12
m2 = 1500
u2 = velocity of car = ?
V = velcity of bus and car after collision
The first step is to calculate V
since the car bus and car came to rest after the collision, it means that
final velocity of bus and car, v3 = 0
distance travelled by bus and car = 10.3
If the frictional force that stopped the bus and car from moving further is 1050, it means that the force that caused the acceleration is equal to the frictional force. Recall,
Force = mass x acceleration
acceleration = force/mass
acceleration = 1050/(3300 + 1500) = 1050/4800 = 0.21875 m/s^2
This means that the bus and car were accelerating at 0.21875 m/s^2 until they came to rest. We would calculate V by applying one of Newton's formula for motion which is expressed as
v^2 = u^2 + 2as
where
v = final velocity
u = initial velocity
a = acceleration
s = distance covered
From the information available,
v = 0
V = u = ?
a = - 0.21875 because the bus and the car were decelerating
s = 10.3
By substituting these values into the formula,
0^2 = V^2 + 2 x - 0.21875 x 10.3
V^2 = 4.50625
V = square root of 4.50625
V = 2.12
Finally, we would input V = 2.12 into the momentum equation. We have
3300 x 12 - 1500 x u2 = (3300 + 1500)2.12
39600 - 1500u2 = 10176
1500u2 = 39600 - 10176 = 29424
u2 = 29424/1500
u2 = 19.616
The car was moving at a velocity of 19.616 m/s.
If the speed limit is 15 m/s, it means that the driver was driving above the speed limit. Thus, the driver was not telling the truth