Question

An object at rest is acted by a 8.0N force for 0.40s after this time interval, the object has a final speed of 8.0m/s. How much time is needed for 4.0N force to produce the same speed?

Answer 1

The acceleration of the object

$$a=\frac{\Delta v}{\Delta t}=\frac{8-0}{0.4}=20\:\rm m/s^2$$

So, the mass of the object

$$m=\frac{F}{a}=\frac{8\:\rm N}{20\;\rm m/s^2}=0.4\:\rm kg$$

If the force is reduced by half, the acceleration of the object

$$a=\frac{F}{m}=\frac{4\:\rm N}{0.4\:\rm kg}=10\: \rm m/s^2$$

Therefore, the interval of time

$$\Delta t=\frac{\Delta v}{a}=\frac{8-0}{10}=0.8\:\rm s$$