Car with mass of 1500kg and thrust of 4000N

[jtwitty]

Sorry; this is like soooooooo hard

Homework Statement

A car with a mass of 1500 kg has en engine which can produce 4000N of thrust. Assume that the air resistance on the car is a constant 500N. If the car starts from rest, how fast will it be moving after 10 seconds.

Homework Equations

d=1/2at²+vit
a=f/m

The Attempt at a Solution

a = 4000 / 15000
a = .2666666666666666666666666666666666666666666666666666666666
thats about as far as i can get because that a has to be wrong?

 

[jtwitty]

heres what i just came up with

netforce = 4000 - 500 = 3500

a = 3500/1500
a = 2.4

d= 1/2a(100)
d=120m

a = vf /t
vf = 24

??

 

[Clever-Name]

First you need to determine what the NET force will be on the car. In this case you have 4000N of thrust in the positive x direction (indicate as 'right' on your free body diagram), you also have a 500N resistive force due to air drag (left).

Your net force will be 4000N-500N (3500N).

Since $F = ma$, $a = \frac{F}{m} = \frac{3500}{1500} = 2.33333$

Remember to look at the units of the values you are given. For some reason you added another 0 to your mass, which is why you got that strange value for a.

From that value of a you should be able to determine the velocity now after 10 seconds, use constant acceleration forumlae.

Edit - ninja'd.

Edit2 - One small correction to your answer. Since 3500/1500 = 2.33333333, rounding up to 2.4 is incorrect. 2.3 would be the appropriate value if significant figures aren't important for this problem. Thus your final answer would be 23m/s

 

[jtwitty]

haha )

thanks so much man :)

 

[rwisz]

As a scientist, it is important to approach problems with a systematic and analytical mindset. In this case, we can use the equations of motion to determine the speed of the car after 10 seconds.

First, we can calculate the acceleration of the car using the formula a = F/m, where F is the net force acting on the car and m is its mass. In this case, the net force is the difference between the engine thrust (4000N) and the air resistance (500N). So, a = (4000N - 500N) / 1500kg = 2.33 m/s2.

Next, we can use the equation d = 1/2at2 + vit to calculate the distance traveled by the car after 10 seconds. Since the car starts from rest, the initial velocity (vi) is 0. So, d = 1/2(2.33 m/s2)(10 s)2 = 116.5 m.

Finally, we can use the equation v = vi + at to calculate the final velocity (vf) of the car after 10 seconds. Again, since the initial velocity is 0, vf = 0 + (2.33 m/s2)(10 s) = 23.3 m/s.

Therefore, after 10 seconds, the car will be moving at a speed of 23.3 m/s. It is important to note that this is a simplified calculation and does not take into account factors such as the changing mass of the car as fuel is consumed, and the effects of friction and air resistance.