Question

5. A racing car accelerates from 50 m/s to 65 m/s in 15 seconds. If the unbalancedforce causing the acceleration is 6,000.0 N, what is the mass of the racing car?

Answer 1

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:

`v_f=v_0+at`

Where:

`\begin{gathered} v_f=\text{ final velocity} \\ v_0=\text{ initial velocity} \\ a=\text{ acceleration} \\ t=\text{ time} \end{gathered}`

We solve for the acceleration first by subtracting the initial velocity from both sides:

`v_f-v_0=at`

Now we divide both sides by "t":

`(v_f-v_0)/(t)=a`

Now we plug in the known values:

`(65(m)/(s)-50(m)/(s))/(15s)=a`

Now we solve the operations, we get:

`1(m)/(s^2)=a`

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:

`F=ma`

Now we solve for the mass by dividing both sides by the acceleration:

`(F)/(a)=m`

Now we plug in the values:

`(6000N)/((1m)/(s^2))=m`

Solving the operations we get:

Therefore, the mass of the car is 6000 kilograms.