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The velocity-time graph for a cycle is shown. a) Work out the distance travelled on the cycle in the first 14 seconds. b) Work out the acceleration in the first 4 seconds.

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The velocity-time graph for a cycle is shown. a) Work out the distance travelled on the cycle in the first 14 seconds. b) Work out the acceleration in the first 4 seconds.

The velocity-time graph for a cycle is shown. a) Work out the distance travelled on the cycle in the first 14 seconds. b) Work out the acceleration in the first 4 seconds.

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QuentinMaster · Tutor for 5 years

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a) The distance travelled in the first 14 seconds is given by the formula \( \frac{1}{2} \times \text{base} \times \text{height} \). Without the specific values from the graph, I can't provide a numerical answer.<br /><br />b) The acceleration in the first 4 seconds is given by the formula \( \frac{\text{change in velocity}}{\text{change in time}} \). Without the specific values from the graph, I can't provide a numerical answer.

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## Step 1: Understanding the problem<br />The problem involves two parts: calculating the distance travelled in the first 14 seconds and calculating the acceleration in the first 4 seconds. Both of these calculations involve understanding the concepts of velocity, time, distance, and acceleration. <br /><br />## Step 2: Calculating the distance travelled in the first 14 seconds<br />The distance travelled by an object is the area under the velocity-time graph. In the first 14 seconds, the graph is a triangle. The area of a triangle is given by the formula \( \frac{1}{2} \times \text{base} \times \text{height} \).<br /><br />### Formula: \( \text{Distance} = \frac{1}{2} \times \text{base} \times \text{height} \)<br /><br />## Step 3: Calculating the acceleration in the first 4 seconds<br />Acceleration is the rate of change of velocity with respect to time. It can be calculated from the slope of the velocity-time graph. In the first 4 seconds, the graph is a straight line, so the acceleration is constant. The slope of a line is given by the formula \( \frac{\text{change in y}}{\text{change in x}} \), where y represents velocity and x represents time.<br /><br />### Formula: \( \text{Acceleration} = \frac{\text{change in velocity}}{\text{change in time}} \)
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