(i) To draw the velocity-time graph, you would start by drawing a straight line from the origin (0,0) to the point (10,20) on the graph. This represents the speedboat accelerating from rest to 20 m/s over 10 seconds. Then, draw a horizontal line from the point (10,20) to (15,20) to represent the speedboat moving at a constant velocity for 5 seconds. Finally, draw a straight line from the point (15,20) back to the x-axis at point (19,0) to represent the speedboat decelerating to a stop over 4 seconds.

(ii) To estimate the velocity of the speedboat after 6 seconds, you would look at the point on the graph where x=6. This falls on the initial straight line, so the speedboat is still accelerating. Since the line is linear, you can estimate the velocity by finding the value of y at x=6. The line goes from 0 to 20 m/s over 10 seconds, so each second corresponds to an increase of 2 m/s (20 m/s ÷ 10 s). Therefore, after 6 seconds, the speedboat would be moving at approximately 12 m/s (6 s × 2 m/s/s).

(iii) The acceleration of the boat during the first 10 seconds can be calculated using the formula for acceleration, which is change in velocity divided by time. The change in velocity is 20 m/s (final velocity) minus 0 m/s (initial velocity), which is 20 m/s. The time is 10 seconds. So, the acceleration is 20 m/s ÷ 10 s = 2 m/s².

(iv) The distance travelled by the boat when it was moving at a constant velocity can be calculated using the formula for distance, which is velocity times time. The velocity is 20 m/s and the time is 5 seconds. So, the distance is 20 m/s × 5 s = 100 m.

Question

(i) To draw the velocity-time graph, you would start by drawing a straight line from the origin (0,0) to the point (10,20) on the graph. This represents the speedboat accelerating from rest to 20 m/s over 10 seconds. Then, draw a horizontal line from the point (10,20) to (15,20) to represent the speedboat moving at a constant velocity for 5 seconds. Finally, draw a straight line from the point (15,20) back to the x-axis at point (19,0) to represent the speedboat decelerating to a stop over 4 seconds.

(ii) To estimate the velocity of the speedboat after 6 seconds, you would look at the point on the graph where x=6. This falls on the initial straight line, so the speedboat is still accelerating. Since the line is linear, you can estimate the velocity by finding the value of y at x=6. The line goes from 0 to 20 m/s over 10 seconds, so each second corresponds to an increase of 2 m/s (20 m/s ÷ 10 s). Therefore, after 6 seconds, the speedboat would be moving at approximately 12 m/s (6 s × 2 m/s/s).

(iii) The acceleration of the boat during the first 10 seconds can be calculated using the formula for acceleration, which is change in velocity divided by time. The change in velocity is 20 m/s (final velocity) minus 0 m/s (initial velocity), which is 20 m/s. The time is 10 seconds. So, the acceleration is 20 m/s ÷ 10 s = 2 m/s².

(iv) The distance travelled by the boat when it was moving at a constant velocity can be calculated using the formula for distance, which is velocity times time. The velocity is 20 m/s and the time is 5 seconds. So, the distance is 20 m/s × 5 s = 100 m.

Knowee AI · Accepted Answer

(i) To draw the velocity-time graph, you would start by drawing a straight line from the origin (0,0) to the point (10,20) on the graph. This represents the speedboat accelerating from rest to 20 m/s over 10 seconds. Then, draw a horizontal line from the point (10,20) to (15,20) to represent the speedboat moving at a constant velocity for 5 seconds. Finally, draw a straight line from the point (15,20) back to the x-axis at point (19,0) to represent the speedboat decelerating to a stop over 4 seconds.

(ii) To estimate the velocity of the speedboat after 6 seconds, you would look at the point on the graph where x=6. This falls on the initial straight line, so the speedboat is still accelerating. Since the line is linear, you can estimate the velocity by finding the value of y at x=6. The line goes from 0 to 20 m/s over 10 seconds, so each second corresponds to an increase of 2 m/s (20 m/s ÷ 10 s). Therefore, after 6 seconds, the speedboat would be moving at approximately 12 m/s (6 s × 2 m/s/s).

(iii) The acceleration of the boat during the first 10 seconds can be calculated using the formula for acceleration, which is change in velocity divided by time. The change in velocity is 20 m/s (final velocity) minus 0 m/s (initial velocity), which is 20 m/s. The time is 10 seconds. So, the acceleration is 20 m/s ÷ 10 s = 2 m/s².

(iv) The distance travelled by the boat when it was moving at a constant velocity can be calculated using the formula for distance, which is velocity times time. The velocity is 20 m/s and the time is 5 seconds. So, the distance is 20 m/s × 5 s = 100 m.

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