Questions: (b) Fig. 1.1 shows a graph of speed against time for a train. After 100 s the train stops at a station. Fig. 1.1 (i) For the time interval between 40 s and 100 s , calculate the distance travelled by the train.

(b) Fig. 1.1 shows a graph of speed against time for a train. After 100 s the train stops at a station.

Fig. 1.1
(i) For the time interval between 40 s and 100 s , calculate the distance travelled by the train.

Transcript text: (b) Fig. 1.1 shows a graph of speed against time for a train. After 100 s the train stops at a station. Fig. 1.1 (i) For the time interval between 40 s and 100 s , calculate the distance travelled by the train.

Solution

Solution Steps

Step 1: Identify the relevant section of the graph

The problem asks for the distance traveled by the train between 40s and 100s. From the graph, we can see that the speed decreases linearly from 25 m/s at 40s to 0 m/s at 100s.

Step 2: Calculate the area under the graph

The area under the speed-time graph represents the distance traveled. The section of the graph between 40s and 100s forms a trapezoid. The formula for the area of a trapezoid is: \[ \text{Area} = \frac{1}{2} \times (a + b) \times h \] where \( a \) and \( b \) are the lengths of the parallel sides (speeds at 40s and 100s), and \( h \) is the height (time interval).

Step 3: Substitute the values into the formula

Speed at 40s (\( a \)) = 25 m/s
Speed at 100s (\( b \)) = 0 m/s
Time interval (\( h \)) = 100s - 40s = 60s

\[ \text{Area} = \frac{1}{2} \times (25 + 0) \times 60 \] \[ \text{Area} = \frac{1}{2} \times 25 \times 60 \] \[ \text{Area} = 12.5 \times 60 \] \[ \text{Area} = 750 \]