The car

The car weight 1280 kg, increased its speed from 7.3 m/s to 63 km/h on a track of 37.2 m. What force did the car engine have to exert?

Correct answer:

F =  4352 N

Step-by-step explanation:

$$\begin{gathered} m=1280\text{ kg } \\ {v}_1=7.3\text{ m/s } \\ {v}_2=63\text{ km/h}\to \text{ m/s}=63\mathrm{/}3.6\text{ m/s}=17.5\text{ m/s } \\ s=37.2\text{ m } \\ s=v_1\cdot t+{\displaystyle \frac{1}{2}}\cdot a\cdot t^2 \\ {v}_2=v_1+a\cdot t \\ {v}_2-v_1=at \\ s=v_1\cdot t+{\displaystyle \frac{1}{2}}\cdot (v_2-v_1)\cdot t \\ t={\displaystyle \frac{2\cdot s}{2\cdot v_1+v_2-v_1}} \\ t={\displaystyle \frac{2\cdot s}{v_1+v_2}}={\displaystyle \frac{2\cdot 37.2}{7.3+17.5}}=3\text{ s } \\ a={\displaystyle \frac{v_2-v_1}{t}}={\displaystyle \frac{17.5-7.3}{3}}={\displaystyle \frac{17}{5}}=3.4{\text{m/s}}^2 \\ F=m\cdot a=1280\cdot 3.4=4352\text{ N } \\ \text{ Verifying Solution: } \\ {s}_2=v_1\cdot t+{\displaystyle \frac{1}{2}}\cdot a\cdot t^2=7.3\cdot 3+{\displaystyle \frac{1}{2}}\cdot 3.4\cdot 3^2={\displaystyle \frac{186}{5}}=37.2\text{ m} \end{gathered}$$

Try another example

Related math problems and questions:

• Car
  At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
• The bridge
  A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that
• Accelerated motion - mechanics
  The delivery truck with a total weight of 3.6 t accelerates from 76km/h to 130km/h in the 0.286 km long way. How much was the force needed to achieve this acceleration?
• Deceleration of car
  The car has a speed of 60 km/h and after 100 m journey speed of 40 km/h. What is the deceleration of a car if we assume that its movement is constantly slowed down?
• Elevator
  In homes with more floor elevators are used. For passenger transport, the most commonly used traction elevator counterweight. The top of the shaft engine room with the engine. The car is suspended on a rope, which is guided up over two pulleys to the coun
• Acceleration
  The car accelerates at rate 0.5m/s². How long travels 400 meters and what will be its speed?
• Two boys
  Two boys weighing 60kg and 90kg move on roller skates and are attracted to each other by a rope. One boy exerts a force of 15N. What force does the other boy exert? What accelerations will the boys gain? Do not consider friction or air resistance.
• Brakes
  The braking efficiency of a passenger car is required to stop at 12.5 m at an initial speed of 40 km/h. What is the acceleration braking by brakes?
• Where and when
  The truck left Kremnica at 11:00 h at a speed of 60km/h. At 12:30 h, the passenger car started at an average speed of 80km/h. How many kilometers from Kremnica will the passenger car reach truck, and when?
• Speed of car
  The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
• Brakes of a car
  For the brakes of a passenger car to be effective, it is prescribed that a car moving on a horizontal road at a speed of 40 km. A car must stop on the track 15.4 m. What is the deceleration of the car?
• Chained winch
  When digging a well, a chained winch is used to balance the material. An empty shackle weighs 8 kg, a full 64 kg. What force must the worker exert on the crank handle when pulling the shackle with a uniform movement from a depth of 5 m if the shaft diamet
• G forces
  Calculate deceleration of car (as multiple of gravitational acceleration g = 9.81 m/s²) occurs when a vehicle in a frontal collision slows down uniformly from a speed 111 km/h to 0 km/h in 1.2 meters trajectory.
• Express train
  International express train drove from Kosice to Teplice. In the first 279 km, the track was repaired, and therefore it was moving at a speed of 10km/h less than it was scheduled to drive. The rest of the 465 km trip has increased the speed by 8 km/h than
• The swing
  To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart?
• A stone
  There is a stone weighing 60 kg on the billet. The distance from the support point to the stone is 20cm. The length of the billet is 1m. Determine the force exerted by the hand at the end of the billet.
• A steel
  A steel hammer with a weight of 0.5 kg hits the nail at a speed of 3 m/s. How deep the nail penetrates the wood if the hammer acts on the nail with an average force of 50N.