Question

A compact car has a maximum acceleration of 4.0 m/s2 when it carries only the driver and has a total mass of 1200 kg . you may want to review ( pages 108 - 109) . part a what is its maximum acceleration after picking up four passengers and their luggage, adding an additional 400 kg of mass?

Answer 1

Answer : The maximum acceleration will be 3.0 $m/sec^{2}$.

Explanation : We can calculate the force using the formula given below;

F = m . a ;

(F - Force; m - mass and a - acceleration);

given in the problem; mass (1) - 1200 kg; acceleration (1) - 4 $m/sec^{2}$

So, on substituting we get,

F = $m_{1} a_{1}$ = 1200 X 4 = 4800 N; we get F = 4800 N

Now, when mass 400 kg is added then mass (2) will be 1600 kg and acceleration has to be found;

Here, the force remains the same; so it can be equated;

$m_{1} a_{1}$ = $m_{2} a_{2}$;

So, 1200 X 4 = (1200 + 400) x $a_{2}$

Therefore, the answer will be $a_{2}$ = 3.0 $m/sec^{2}$

Answer 2

Let F be the maximum thrust of the car's engine. Then F = ma = 1300 x 3.0 = 3900N. With the added load, F remains the same, but we now have F = 1700a giving a = F/1700 = 3900/1700 = 2.3 m/s².