What average force is required to stop a 990kg car in 7.8s if the car is traveling at 95km/hr?

Question

anonymous · Answer

So far I've converted the initial velocity to 26.3m/s and now I think I have to choose a kinematic equation right?

anonymous · Answer

I would suggest using Impulse here since we are given time. This eliminates the need to find the distance over which the force acts, as it required in using the Work-Energy Theorem. 

Let's define impulse. $$I = \int\limits F dt$$Note that$$F = {dp \over dt}$$therefore$$I = \int\limits {dp \over dt} dt$$The $dt$ will cancel. $$I = \int\limits dp$$Assuming a constant force, we can approximate the integral as a simple "delta"$$I = \Delta p$$and$$I = F \Delta t$$The two definitions of impulse must be equal, therefore$$F \Delta t = \Delta p$$$p$ is the momentum, which is defined as $p = m \cdot v$$$F \Delta t = (m \cdot v_i - m \cdot v_f)$$Noting that the final velocity, $v_f$ is equal to zero, we have$$F \Delta t = m \cdot v_i$$We know the mass, $m$, the initial velocity $v_i$, and the time $\Delta t$. We can easily solve for the average force $F$.

anonymous · Answer

Neat!

anonymous · Answer

you can use the equation of motion
v= u + at which will give you the acceleration. 

then, Force = mass*acceleration
and thus, you get the average force required

anonymous · Answer

^Okay I was thinking about using this formula, I was unsure between this one and another one of the kinematic equations. Thanks.

anonymous · Answer

I ended up getting -3.3 * 10^4, is that right>?

anonymous · Answer

Yep.

jamesj · Answer

I'd encourage you to read Eashmore's answer, since it contains a good description of the Physics here.  There's always a danger in the sciences of using formulae and forgetting what is really going on.

The formula v = u + at can be deduced from what Eashmore has said, but the advantage of understanding what he has written is you will have more insight into the underlying science.  His approach will also generalize, for instance,  when the acceleration a is not constant while the formula v = u + at does not.

anonymous · Answer

first you find  the applied acceleration for which the car will  stop after the given time and after it you get the value of acceleration and simply you can find the valu of average force by apply newton's second law...look here and apply these formulae:
                                                       v=u-at=>0=u-at=>a=u/t=>a=(95*5/18)/7.8=3.38 m/s2(about).hence F=ma=990*3.38=3346.2N