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Motion and Time - Distance-Time Graphs

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A Distance-Time graph represents the motion of an object in a visual form, where distance is plotted on the Y-axis and time is plotted on the X-axis.

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For an object moving with a uniform speed (constant speed), the distance-time graph is always a straight line passing through the origin.

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The slope or gradient of the distance-time graph represents the speed of the object. A steeper slope indicates a higher speed (vv).

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If the distance-time graph is a horizontal line parallel to the X-axis (Time axis), it means the distance does not change over time, and the object is at rest (Speed = 0 m/s0\ m/s).

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A curved line on a distance-time graph indicates non-uniform motion, where the speed of the object is changing.

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To plot the graph, time is usually considered the independent variable and distance is the dependent variable.

📐Formulae

Speed=DistanceTimeSpeed = \frac{Distance}{Time}

v=dtv = \frac{d}{t}

Slope=Change in distanceChange in time=d2−d1t2−t1Slope = \frac{Change\ in\ distance}{Change\ in\ time} = \frac{d_2 - d_1}{t_2 - t_1}

Distance=Speed×TimeDistance = Speed \times Time

💡Examples

Problem 1:

From a distance-time graph, a cyclist is seen to cover a distance of 30 m30\ m in 6 s6\ s at a constant speed. Calculate the speed and describe the shape of the graph.

Solution:

Given: Distance=30 mDistance = 30\ m, Time=6 sTime = 6\ s. Using the formula v=dtv = \frac{d}{t}, we get v=30 m6 s=5 m/sv = \frac{30\ m}{6\ s} = 5\ m/s.

Explanation:

Since the speed is constant at 5 m/s5\ m/s, the distance-time graph will be a straight line starting from the origin (0,0)(0,0) and passing through the point (6,30)(6, 30).

Problem 2:

A car's position on a graph stays at 15 km15\ km for the time interval between t=2 ht = 2\ h and t=5 ht = 5\ h. What is the speed of the car during this interval?

Solution:

v=d2−d1t2−t1=15 km−15 km5 h−2 h=0 km3 h=0 km/hv = \frac{d_2 - d_1}{t_2 - t_1} = \frac{15\ km - 15\ km}{5\ h - 2\ h} = \frac{0\ km}{3\ h} = 0\ km/h.

Explanation:

Because the distance does not change as time passes, the graph is a horizontal line. This indicates the car is stationary (at rest).

Distance-Time Graphs - Revision Notes & Key Formulas | CBSE Class 7 Science