Answered

Discover new information and insights with the help of IDNLearn.com. Ask any question and get a detailed, reliable answer from our community of experts.

A car with weight of 7,656newton is moving with 43.13km/h. The driver applies thebreaks to stop the car in 9.38seconds. The magnitude of theforce (in newton) needed tostop the car is:

Sagot :

Givens.

• Weight = 7,656 N.

,

• Initial speed = 43.13 km/h.

,

• Time = 9.38 seconds.

,

• Final speed = 0 km/h. (The car stops)

First, find the acceleration involved.

[tex]\begin{gathered} v_f=v_0+at \\ a=\frac{v_f-v_0}{t} \\ a=\frac{0-43.13\cdot\frac{km}{h}}{9.38\sec } \end{gathered}[/tex]

But, we need to transform the initial speed to meters per second.

[tex]43.13\cdot\frac{km}{h}\cdot\frac{1000m}{1\operatorname{km}}\cdot\frac{1h}{3600\sec}=11.98\cdot\frac{m}{s}[/tex]

Now we can proceed to find the acceleration.

[tex]\begin{gathered} a=\frac{-11.98\cdot\frac{m}{s}}{9.38s} \\ a=-1.28\cdot\frac{m}{s^2} \end{gathered}[/tex]

Once you have the acceleration. Find the mass of the car using the weight formula.

[tex]\begin{gathered} W=mg \\ 7,656N=m\cdot9.8\cdot\frac{m}{s^2} \\ m=\frac{7,656N}{9.8\cdot\frac{m}{s^2}} \\ m=781.22\operatorname{kg} \end{gathered}[/tex]

Then, use Newton's Second Law to find the needed force to stop.

[tex]\begin{gathered} F=ma \\ F=781.22\operatorname{kg}\cdot(-1.28\cdot\frac{m}{s^2}) \\ F=-999.96N \end{gathered}[/tex]

Therefore, the magnitude of the force needed to stop the car is 999.96 Newtons.

Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.