Question

In: Physics

A 2000 kg car is sitting at a stop sign and begins to accelerate to a...

A 2000 kg car is sitting at a stop sign and begins to accelerate to a speed of 5km/hr at that moment a 1000kg car smashed into the rear end of thus car and stuck together in the collision. A cop shows up to the scene and assumes the 1000 kg car was speeding at 50km/hr by measuring the tire marks that are 3 m long. Assume the the coefficient of friction is 0.8 what is the speed that the car was going when the accident took place.

Solutions

Expert Solution

The frictional force is given by where N is the normal force

After the two cars are stuck together, where m_1 and m_2 are the masses of the two cars

Therefore

The deceleration due to this force on the combined system of the two cars is

Substituting the value of the coefficient of friction

deceleration is

Let the initial velocity of the combined two-car system right after the collision be

Based on the tire marks, it came to rest after a displacement of and

Since acceleration is opposite to the direction of motion, it is negative

Use Newton's equation of motion

Substituting values

Therefore

Converting units,

This is the speed of the combined two car system right after the collision

Since momentum is conserved even in an inelastic collision, we have the momentum conservation equation

where v_1 and v_2 are the velocities of the two cars right before the collision

We know m_1 had a speed of v_1=5km/hr right before the collision.

Putting this back to the equation

Rearranging,

Therefore, the 1000kg car was speeding at 64.1km/hr when the accident took place

genius_generous answered 3 years ago
Next > < Previous

Related Solutions

A car sitting at a red light begins to accelerate at 2 m/s2 when the light...
A car sitting at a red light begins to accelerate at 2 m/s2 when the light turns green. It continues with this acceleration until it reaches a speed of 20 m/s. It then travels at this speed for another few minutes. How far does the car travel in the first 50 s after the light changes to green?
A car starts from rest at a stop sign. It accelerates at 5.56 m/s2 for 6.56...
A car starts from rest at a stop sign. It accelerates at 5.56 m/s2 for 6.56 seconds, coasts for 3.6 s, and then slows down at a rate of 3.93 m/s2 for the next stop sign. How far apart are the stop signs?
A car starts from rest at a stop sign. It accelerates at 2.0 m/s2 for 6.3...
A car starts from rest at a stop sign. It accelerates at 2.0 m/s2 for 6.3 seconds, coasts for 3.0 s , and then slows down at a rate of 1.5m/s2 for the next stop sign. a) How far apart are the stop signs? Express your answer with the appropriate units.
A car starts from rest at a stop sign. It accelerates at 4.4 m/s^2 for 6.9...
A car starts from rest at a stop sign. It accelerates at 4.4 m/s^2 for 6.9 s, coasts for 2.3 s, and then slows down at a rate of 3.4 m/s^2 for the next stop sign. How far apart are the stop signs?
Two cars collide at an intersection. Car A, with a mass of 2000 kg , is...
Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1400 kg , is going from north to south at 14.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of...
Two cars collide at an intersection. Car A, with a mass of 2000 kg , is...
Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1300 kg , is going from north to south at 17.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of...
1.a) What is the (average) power needed to accelerate a car of mass m=1550 kg from...
1.a) What is the (average) power needed to accelerate a car of mass m=1550 kg from zero to 60 mph in 7.1 s? b) Which simplifications did you make in that short calculation, i.e. what did you neglect? 2.The current BC hydro rates are 6.55 cents per kWh. If you have a desktop computer that uses 200 W (on average), how much does it cost you per month to run it for 6 hours per day? 3. An elevator car...
Car A has a mass of 2000 kg and speed of 10 miles per hour. Car...
Car A has a mass of 2000 kg and speed of 10 miles per hour. Car B has mass of 1000 kg and speed of 30 miles per hour. The two cars collide to each other and stick together after collision in three different situations. Calculate the velocity of the two cars after the collision. 1. Car A moves East and car B moves West and had a head to head collision. Calculate the velocity of the two cars after...
A sports car of mass 1000 kg can accelerate from rest to 72. km/h in 6.6...
A sports car of mass 1000 kg can accelerate from rest to 72. km/h in 6.6 s. a) What would the average force of the car's engine be? b) If the same force acts on 2000 kg car what is the acceleration.
A 1450 kg car begins sliding down a 12.0 ° inclined road with a speed of...
A 1450 kg car begins sliding down a 12.0 ° inclined road with a speed of 34.0 km/h.The engine is turned off, and the only forces acting on the car are a net frictional force from the road and the gravitational force. After the car has traveled 45.0 m along the road, its speed is 50.0 km/h. (a) How much is the mechanical energy of the car reduced because of the net frictional force? (b) What is the magnitude of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT