An object moves forward at 10 metres per second for four seconds and then moves backward for two seconds at the same speed. What net forward distance does the object move from its starting point?
Let’s start by underlining the important bits of the question. So we’ve got an object. It moves forward at 10 metres per second for four seconds and then it moves backward for two seconds at the same speed. What we’re asked to do is to find out the net forward distance that the object has moved from its starting point.
So let’s say that the object’s starting point is here on the screen. We know that it is moving at 10 metres per second forward initially. This means that every second it moves 10 metres. And it continues moving forward for four seconds. So we start here. Then, in one second, it is moved 10 metres. In two seconds, it is moved another 10 metres. In three seconds, it is moved yet another 10 metres. And in four seconds, it is moved the final 10 metres. So that’s 10 metres plus 10 metres plus 10 metres plus 10 metres. That’s 40 metres. In other words, from its starting point, it is moved 40 metres in four seconds.
Then we know that the object starts moving backward at the same speed. But it only does this for two seconds. So it moves back 10 metres in one second and another 10 metres in two seconds. This is where it ends. So that’s 10 metres and another 10 metres. That’s 20 metres.
What we want to do is to find the net forward distance. What this means is that the distance overall that the object has travelled from start to finish. In other words, this is the distance that we’re looking for. Well, that distance is just the 40 metres it travelled initially forward minus the 20 it travelled back or in other words, the net distance travelled is 20 metres. So our final answer is that the object travels a net forward distance of 20 metres.
By the way, it is important to note that the net distance travelled is only dependent on the starting point and the finishing point. This means that hypothetically the object could have taken any path it wanted to. It could have for example started by going backward and then forward again. It could have even gone side to side if it wanted to.
As long as it starts at the start point and finishes at the finish point, it doesn’t matter what path it took to get there. The net distance is the shortest distance between the start point and the finish point. That’s a straight line.
So even if the object took the red path that we’ve drawn, the net distance forward that it would have moved would still be 20 metres. That’s because the start point and the finish point of the red path are exactly the same as the start point and the finish point of the orange and blue paths.