The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be________.

Solution

Physics sir · 3 steps

On a speed-time graph, distance is the area under the line, and here that area is one triangle.

1. Read the graph. The speed rises in a straight line from 0 at t = 0 to 8 m s⁻¹ at t = 5 s. Speed is never negative, so the area under the graph gives the distance.
2. Shape of the area. The region between the line and the time axis is a right triangle. Its base is 5 s and its height is 8 m s⁻¹.

   d = 1/2 × 5 s × 8 m s⁻¹ = 20 m

3. So. The particle travels 20 m in the first 5 s.

The common slip: 40. Multiplying the final speed by the time without the factor 1/2 gives 40 m. The particle was slower than 8 m s⁻¹ for the whole 5 s, so use the average speed, 4 m s⁻¹.

The idea to keep. Area under a speed-time graph is distance. Break it into triangles and rectangles. If speed changes uniformly, use average speed times time.

Answer from the NTA final answer key. Solution by PrepWiser.