Respuesta :
We are given that a car accelerates from 50 m/s to 65m/s in 15 seconds. To determine the force that causes the acceleration we need to determine first the acceleration of the car. To do that we will use the following equation of motion:
[tex]v_f=v_0+at[/tex]Where:
[tex]\begin{gathered} v_f=\text{ final velocity} \\ v_0=\text{ initial velocity} \\ a=\text{ acceleration} \\ t=\text{ time} \end{gathered}[/tex]We solve for the acceleration first by subtracting the initial velocity from both sides:
[tex]v_f-v_0=at[/tex]Now we divide both sides by "t":
[tex]\frac{v_f-v_0}{t}=a[/tex]Now we plug in the known values:
[tex]\frac{65\frac{m}{s}-50\frac{m}{s}}{15s}=a[/tex]Now we solve the operations, we get:
[tex]1\frac{m}{s^2}=a[/tex]Now, we use Newton's second law to determine the mass. The law states that the force of an object is directly proportional to its mass. This can be written mathematically as:
[tex]F=ma[/tex]Now we solve for the mass by dividing both sides by the acceleration:
[tex]\frac{F}{a}=m[/tex]Now we plug in the values:
[tex]\frac{6000N}{\frac{1m}{s^2}}=m[/tex]Solving the operations we get:
[tex]6000\operatorname{kg}=m[/tex]Therefore, the mass of the car is 6000 kilograms.
