A dog starts at the origin and runs forward at 6m/s for 1.5s and then turns around to fetch the ball by running backward at 7m/s for 3s. If the dog runs back to the origin at 4m/s the how much time has elapsed between the start and when he returns with the ball

Total time elapsed between the start and when he returns with the ball is 7.5s

Explanation:

From the question,

- The dog starts at the origin and runs forward at 6m/s for 1.5s. First, we will determine the distance covered while running forward.

From

Speed = Distance / Time

Distance = Speed × Time

Speed = 6m/s

Time = 1.5s

∴ Distance = 6m/s × 1.5s

Distance = 9m

That is, the dog covered a distance of 9m while running forward.

- The dog turns around and runs backward at 7m/s for 3s. Now, we will also determine the distance the dog covered backwards.

Distance = Speed × Time

Speed = 7m/s

Time = 3s

Distance = 7m/s × 3s

Distance = 21m

The dog's displacement from the origin is 21m - 9m = 12m

Now, to calculate how much time has elapsed between the start if the dog runs back to the origin at 4m/s, we will first determine the time the dog spent back to the origin and then add to the time spent for the first two distances.

To get back to the origin, the dog needs to cover 12m

From

Speed = Distance / Time

Time = Distance / Speed

Distance = 12m

Speed = 4m/s

∴ Time = (12m) / (4m/s)

Time = 3s

Therefore, the dog spent 3s to run back to the origin.

Hence, total time elapsed = 1.5s + 3s + 3s

Total time elapsed = 7.5s

a straight line sloped