A tank of 41 metric tons started moving along a section of horizontal ground. The resistance to its motion was nine newtons per metric ton of its mass, and the magnitude of the force generated by its engine was 1450 newtons. Determine the tank’s speed 472 seconds after it started moving, rounding the result to the nearest two decimal places.
We will begin by sketching a diagram to model the situation. We are told that the tank has a mass of 41 metric tons. And as there are 1000 kilograms in a ton, this is equal to 41000 kilograms. We are told the resistance to motion was nine newtons per metric ton, and nine multiplied by 41 is 369. The resistance force acting against the motion is 369 newtons. We are also told that the force generated by the engine is 1450 newtons. We can use these forces together with Newton’s second law, force is equal to mass multiplied by acceleration, to calculate the acceleration of the tank.
Taking the direction the tank is moving to be positive, the sum of the forces is equal to 1450 minus 369. This is equal to 41000 multiplied by 𝑎. Dividing through by 41000, we have 𝑎 is equal to 1081 over 41000. This is the acceleration of the tank in meters per second squared. We can now use the equations of motion or SUVAT equations to determine the tank’s speed after 472 seconds.
We know that the initial speed 𝑢 is equal to zero meters per second as the tank starts from rest. We have just calculated 𝑎 is equal to 1081 over 41000 meters per second squared. We need to calculate the tank’s speed or final velocity 𝑣 after 472 seconds. We will use the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡. Substituting in our values, we have 𝑣 is equal to zero plus 1081 over 41000 multiplied by 472. This is equal to 12.4446 and so on.
As we are asked to round our answer to two decimal places, 𝑣 is equal to 12.44. The tank’s speed 472 seconds after it started moving rounded to two decimal places is 12.44 meters per second.