Question

How long does it take to  stop a 1000 kg object moving at 20 m/s with a force 5000N? 2500 N, 1000 N, 500 N, 400 N, 200 N, 100 N

Answer 1

`\begin{gathered} 5000N\Rightarrow4s \\ 2500N=8s \end{gathered}`

Step-by-step explanation

To find the time taken to stop the object, we first have to find the acceleration of the object.

Since the force is working to stop the object (slow down the object), it means that the object is decelerating (slowing down).

To find the acceleration (deceleration), apply Newton's second law of motion:

`F=ma`

where F = force; m = mass; a = acceleration

Therefore, for a force of 5000N, we have that:

`\begin{gathered} 5000=1000\cdot a \\ \Rightarrow(5000)/(1000)=a \\ \Rightarrow a=5m\/s^2 \end{gathered}`

Now, we can apply Newton's equation of motion to find the time taken to stop the object:

`v=u-at`

where v = final velocity = 0 m/s; u = initial velocity = 20 m/s; t = time taken

Note: the negative sign indicates deceleration

Hence, the time taken for a force of 5000N to stop the object is:

`\begin{gathered} 0=20-5\cdot t \\ \Rightarrow5t=20 \\ \Rightarrow t=(20)/(5) \\ t=4s \end{gathered}`

For a force of 2500N, the deceleration is:

`\begin{gathered} 2500=1000\cdot a \\ a=(2500)/(1000) \\ a=2.5m\/s^2 \end{gathered}`

Hence, the time taken for a force of 2500N to stop the object is:

`\begin{gathered} 0=20-2.5\cdot t \\ \Rightarrow2.5t=20 \\ t=(20)/(2.5) \\ t=8s \end{gathered}`