Motion And Time

CloseSpeed is defined as distance divided by time. If you rearrange this formula, time taken equals distance divided by speed. For example, if a car has to cover 100 kilometre at a speed of 50 kilometre per hour, the time taken will be 100/50 = 2 hour.

CloseAn odometer is a device fitted in the dashboard of a vehicle. It records the total distance the vehicle has travelled since it was manufactured, usually in kilometre. It does not measure speed directly; a speedometer measures speed.

CloseUsing the formula time taken = distance / speed. Here distance = 120 km, speed = 40 km/h. So time = 120/40 = 3 hour. This means the car will need 3 hour to complete the journey.

CloseSpeed = distance / time = 60 km / 3 h = 20 km/h. This is uniform speed if the cyclist does not change pace. For non-uniform motion, this would be the average speed.

CloseA bar graph uses rectangular bars of equal width but different heights to show comparisons among different categories. The height of each bar represents the value of the data, such as the distance covered by different vehicles in one hour.

CloseBy convention, in a distance-time graph, time is taken along the horizontal axis (X-axis) and distance is taken along the vertical axis (Y-axis). This helps us see how distance changes as time passes.

CloseWhen an object moves with uniform (constant) speed, the distance increases by equal amounts in equal intervals of time. On a graph, this gives a straight line that slopes upward. The slope of this line gives the speed.

CloseIf the distance does not change as time increases, the line is horizontal. This means the object is not moving; it is at rest. For example, a parked car will show a horizontal line on a distance-time graph.

CloseSlope is calculated as (change in distance) divided by (change in time). That is exactly the definition of speed. A steeper slope means higher speed, and a gentler slope means lower speed.

CloseA curved line means the speed is changing. The object may be speeding up (increasing slope) or slowing down (decreasing slope). This type of motion is called non-uniform motion.

CloseWhen the bob moves from its mean position to one extreme, back to mean, to the other extreme, and back to mean, it completes one oscillation. This is the basic unit of oscillatory motion.

CloseThe time period is the time required for one full oscillation. It is measured in second. For example, if a swing takes 3 second to go back and forth once, its time period is 3 second.

CloseTime period = total time / number of oscillations = 60 second / 30 = 2 second. So each oscillation takes 2 second.

CloseUniform motion means the object covers equal distances in equal intervals of time. A car moving at constant speed on a straight road does exactly that. The other options involve changing speed, so they are non-uniform.

CloseNon-uniform motion means speed is changing. When a car accelerates, its speed increases with time, so it covers unequal distances in equal intervals of time. The other options involve constant speed, so they are uniform motion.

CloseIn the first hour, speed = 50 km/h. In the next 1.5 hour, speed = 50/1.5 ≈ 33.33 km/h. Since speed is not the same throughout, the motion is non-uniform. The average speed is total distance (100 km) divided by total time (2.5 h) = 40 km/h.

CloseUniform speed means distance increases equally in equal time intervals. This relationship is linear, so the graph is a straight line that goes upward as time increases.

CloseAt rest means distance does not change even when time passes. So the distance remains constant. On a graph, this appears as a flat horizontal line parallel to the time axis.

CloseSlope = (change in distance) / (change in time). This ratio is exactly the speed. A steeper slope means higher speed. You can pick any two points on the straight line and divide the vertical difference by the horizontal difference.

CloseThe odometer shows total distance from the beginning. To find the distance travelled during a trip, subtract the initial reading from the final reading: 1500 km − 1200 km = 300 km.

CloseTime taken = distance / speed = 300 metre / 15 metre per second = 20 second. Remember to keep the units consistent. Here both distance and speed are in metre and metre per second, so the answer is in second.

CloseSpeed = distance / time = 360 km / 4 h = 90 km/h. This is the average speed if the train did not move at exactly the same speed throughout the journey.

CloseBar graphs are ideal for comparing data across different categories, such as the distances covered by a car, bus, bicycle, and train in one hour. Each vehicle gets a separate bar, and the height shows the distance.

CloseTo make a bar graph fair and easy to read, all bars must have the same width. Only the height (or length) of the bars changes according to the value of the data. Unequal widths can mislead the viewer.

CloseA steeper slope means a larger change in distance in the same amount of time. That means the object is moving faster. If the slope keeps increasing, the object is accelerating (non-uniform motion).

CloseA less steep slope means a smaller change in distance in the same amount of time. That means the object is slowing down. The speed is decreasing.

CloseFrequency tells how many complete oscillations happen in one second. If a pendulum makes 5 oscillations in one second, its frequency is 5 hertz (Hz). Time period is the reciprocal of frequency.

CloseTime period = 1 / frequency. If frequency = 2 Hz, then time period = 1/2 = 0.5 second. This means one oscillation takes half a second.

CloseWhen speed changes continuously, distance does not increase at a constant rate. The graph becomes a curve. The shape of the curve tells us whether the object is speeding up (curve bending upward) or slowing down (curve bending downward).

CloseCheck the speed in each part: first part speed = 10/2 = 5 m/s, second part speed = 20/4 = 5 m/s, third part speed = 30/6 = 5 m/s. Since speed is constant (5 m/s) throughout, the motion is uniform.

CloseTotal distance = 100 m + 100 m = 200 m. Total time = 20 s + 30 s = 50 s. Average speed = total distance / total time = 200 m / 50 s = 4 m/s.

CloseFor an object at rest, distance does not change as time changes. So change in distance = 0. Slope = 0 / (change in time) = 0. A horizontal line has zero slope.

CloseDistance = speed × time = 25 m/s × 40 s = 1000 metre. This is equal to 1 kilometre. So the car covers 1 km in 40 second at this speed.

CloseDistance travelled = 2400 km − 2000 km = 400 km. Time taken = 1 hour. Average speed = 400 km / 1 h = 400 km/h. This is a very high speed, possible only for racing cars or aeroplanes.

CloseA distance-time graph shows only the relationship between distance and time. It tells us about motion, rest, speed, and uniformity. It cannot show physical properties like colour, shape, or material of the object.

CloseTime = distance / speed = 15 km / 30 km/h = 0.5 hour. Half an hour is 30 minute. This formula works for any units as long as they are consistent.

CloseA pendulum bob moves back and forth repeatedly about a mean position. This to-and-fro motion is called oscillatory motion. It is also periodic because it repeats after a fixed time interval.

CloseIf distance decreases as time increases, the object is returning toward the starting point. The slope is negative. In most simple cases, we consider only forward motion, so downward slopes are rare in basic distance-time graphs.

CloseA bar graph is best for comparing quantities across different categories. Here each animal is a category, and the distance covered is the value. Bars of equal width with different heights make comparison easy.

CloseSpeed in first part = 200/25 = 8 m/s. Then speed becomes zero during the stop (0 m/s). Then speed in last part = 100/20 = 5 m/s. Since speed changes, the overall motion is non-uniform.

CloseThis is the basic definition of speed. From this formula, we can also write Distance = Speed × Time and Time = Distance / Speed. All three forms are useful depending on what we need to find.

CloseSpeed = distance / time = 240 metre / 12 second = 20 metre per second. Uniform speed means this value is constant throughout the motion.

CloseTime period = total time / number of oscillations = 25 second / 10 = 2.5 second. This means each oscillation takes two and a half seconds.

CloseFrom a distance-time graph, we can calculate speed as the slope. For uniform motion, the slope is constant. For non-uniform motion, the slope at any point gives the instantaneous speed.

CloseSpeed in first 5 s = 50/5 = 10 m/s. Speed in next 5 s = 100/5 = 20 m/s. Speed in last 5 s = 150/5 = 30 m/s. Speed is increasing, so motion is non-uniform and the object is accelerating.

CloseTo convert km/h to m/s, multiply by 5/18. 108 × (5/18) = 108 × 5 ÷ 18 = 540 ÷ 18 = 30 m/s. This is a common conversion in physics problems.

CloseA speedometer shows the instantaneous speed of the vehicle in kilometre per hour or mile per hour. An odometer shows total distance travelled. Do not confuse the two.

CloseSteepness (slope) is change in distance divided by change in time. A larger slope means more distance covered in the same time, which means higher speed.

CloseFirst convert 1 kilometre into metre: 1 km = 1000 metre. Then time = distance / speed = 1000 metre / 5 metre per second = 200 second. That is 3 minute and 20 second.

CloseTime period = total time / number of oscillations = 30 second / 15 = 2 second. The child takes 2 second to swing forward and back once. This is an example of oscillatory motion in daily life.