Calculating Average Net Force of 810-kg Car

[brncsfns5621]

An 810-kg car accelerates from rest to 27m/s in a distance of 120m. What is the magnitude of the average net force acting on the car?

120m / 27m/s= 4.4 s

F=ma
=810kg * 4.4s
= 3600 N

This is not one of my choices. What did I do wrong?

 

[radou]

An 810-kg car accelerates from rest to 27m/s in a distance of 120m. What is the magnitude of the average net force acting on the car?

120m / 27m/s= 4.4 s

F=ma
=810kg * 4.4s
= 3600 N

This is not one of my choices. What did I do wrong?

You can not apply t = s / v, because the car is accelerating. The velocity of the car is given with 27 = a * t. The second equation is the displacement of the car, 120 = 1/2*a*t^2. Now, plug in the first equation into the second one, and get the time and acceleration. Then you can calculate the average force acting on the car.

 

[brncsfns5621]

So, using your equations I get:

120m = 1/2 (27m/s)^2
120m = 1/2 (729m^2/s^2)
120m = 364m^2/s^2
rearrange--> s^2 = 364m^2/120m
s^2 = 3.03m

This isn't right...

 

[brncsfns5621]

Anyone have any info on this?

 

[radou]

Anyone have any info on this?

You have two equations:

(1)... 27 = a*t
(2)... 120 = 1/2*a*t^2

From (1) you obtain a = 27/t. Putting that into (2) gives t = 8.89 seconds, which implies (from (1) ) a = 3.04 m/s^2. Hence, F = m*a implies F = 810 * 3.04 = 2462.4 [N]. Do not mix units with variables. You do not have tu put units (such as m/s, for example) into your equations. In other words, you wrote

...s^2 = 3.03m

This isn't right...

which reads: 'Seconds squared equals 3.03 meters.' Does not make any sense, right?

 

[brncsfns5621]

WOW! I brain farted that one. For some reason I was thinking to replace the "a*t" with 27. Don't know why... Thank you for your help, I really appreciate it.

 

[rainingurl]

solve the problem

a = ?
a = v/t
solve t using d=.5(v-V)t
t= 8.8sec

sub in the equation
a = (27m/s)/8.8sec
a = 3.06m/s^2

F= mass*acceleration
810kg*3.06m/s^2 = 2485N = 2500N

 

[dkzdrood]

KE = 1/2 * m v^2
KE = (1/2) (810) (27^2)
W= deltaKE
W = (1/2) (810) (27^2)
W = force * distance
(1/2)(810)(27^2) = 120*F
F= [(1/2)(810)(27^2)] / (120)
F= 2460.375 N