**Q **1. Write one main difference between speed and velocity.

**Solution**

Speed has only magnitude while velocity has both magnitude and direction.

**Q **2. A body leaving a certain point “O” moves with a constant acceleration. At the end of the 5th second its velocity is 1.5 m/s. At the end of the sixth second the body stops and then begins to move backwards. Find the distance traversed by the body before it stops. Determine the velocity with which the body returns to point “O “?

**Solution**

The velocity slows 1.5 m/s in the sixth second so if the initial velocity direction is positive, the acceleration isa = (dv/dt) = -1.5 m/s². Using the equation, v = u + at and knowing that the return time to zero velocity will equal the approach time of 6 seconds. v = 0 + (- 1.5) × 6 v = -9 m/s So the velocity upon returning to “O” is -9 m/s. The average velocity between “O” and the stop point is v = (9 + 0) / 2 v = 4.5 m/s So the particle travels d = 4.5 × 6 m → d = 27 m between “O” and the stop points.

**Q **3. A bus decreases its speed from 80 km h^{-1} to 60 km h^{-1} in 5 s. Find the acceleration of the bus.

**Solution**

Negative sign indicates the bus is decelarating.

**Q **4. A body travels from A to B in 10 seconds with a speed of 50 km/h and returns with a speed of 100 km/h in 5 s. Find the average speed. Also find the average velocity for the whole journey.

**Solution**

Distance from A to B = Speed x time

= 50 km/h x 10 s

=(50 km/h x 10 s) x (5/18) ….

(to convert km/h to m/s multiply by 5/18)

=1250 / 9

=139 m Total distance from A to B both ways

= 139 m × 2

= 278 m Total time taken = 10 + 5 = 15 s

Displacement is zero, because the body has come back to its initial position.

**Q **5. What is the quantity which is measured by the area occupied below the velocity-time graph?

**Solution**

The distance is measured by the area occupied below the velocity time graph.

**Q **6. Give an example of the motion of a body moving with a constant speed but with a variable velocity. Draw a diagram to represent such a motion

**Solution**

The motion of a body in a circular path with uniform speed has a variable velocity because in the circular path, the direction of motion of the body continuously changes with time.

**Q **7. A scooter starts from rest and travels with a uniform acceleration of 2 ms^{-2} for 6 sec. What is the velocity acquired?

**Solution**

Initial velocity, u =0 (starts from rest) Final velocity, v = ? Time, t =6 s We know that acceleration is a = (v – u)/t Therefore, velocity is v = u + at = 0 + 2 x 6 = 12 m/s

**Q **8. A ball is thrown vertically upwards. It rises up to a height of 20 m and comes back to the initial position. Find: the total distance covered by the ball, and the displacement of the ball.

**Solution**

The total distance travelled = 20 m + 20 m = 40 m. Since, the ball returns to its initial position, the initial and final positions coincide with each other. Hence, the displacement of the ball = 0

**Q **9. Explain average speed.

**Solution**

The ratio of the total distance travelled by the body to the total time of journey is called its average speed. It is also the average of values of speeds evaluated over equal intervals of time. Its SI unit is m/s.

**Q **10. Define the following terms: (a) speed (b) velocity (c) uniform velocity (d) non uniform velocity

**Solution**

Speed Speed is the distance travelled by a body in one second and is measured in metre per second (m s^{-1}) Velocity Velocity is the distance travelled by a body in a particular direction in unit time Or Velocity is defined as the rate of change of displacement. It is measured in metre per second (m s^{-1}) Uniform Velocity A body is said to travel with uniform velocity if it undergoes equal displacement in equal intervals of time, however small in a given direction Non-uniform Velocity A body is said to be moving with non-uniform or variable velocity if it covers unequal distances in equal intervals of time or it covers equal distances in unequal intervals of time or it covers equal distances in equal intervals of time, but its direction is changing.

**Q **11. What is the nature of distance-time graphs for uniform and non-uniform motion of an object?

**Solution**

The distance-time graph for uniform motion is a straight line (inclined at an angle to the time axis). The distance-time graph for non-uniform motion can be a curve with increasing or decreasing slope or any zigzag line.

**Q **12. Distinguish between average speed and average velocity.

**Solution**

Average speed is the ratio of the total distance travelled by the body to the total time of journey, it is never zero. If the velocity of a body moving in a particular direction changes with time, then the ratio of displacement to the time taken in entire journey is called its average velocity. Average velocity of a body can be zero even if its average speed is not zero.

**Q **13. Examine the data given for the motion of two different objects A and B carefully and state whether the motion of the objects is uniform or non uniform. Give reasons. Time Distance travelled by object A in m Distance travelled by object B in m 9.30 a.m 10 12 9.45 a.m 20 19 10.00 a.m 30 23 10.15 a.m 40 35 10.30 a.m 50 37 10.45 a.m 60 41 11.00 a.m 70 44

**Solution**

Motion of object A is uniform because it covers a distance of 10 km in every 15 minutes, that is equal distances in equal intervals of time. Motion of object B is non-uniform because it is covering unequal distances in equal intervals of time.

**Q **14. Give the differences between scalar and vector quantities.

**Solution**

Parameters Scalar Quantities Vector Quantities Definition The physical quantities which have magnitude only are scalars. The physical quantities which have magnitude and direction both are vectors. Example Mass, length, distance, speed, etc. Displacement, velocity, acceleration, etc.

**Q **15. What is the acceleration in the case of uniform velocity ?

**Solution**

In the case of uniform velocity, the speed or direction of a moving object is not changed and thus there is no in acceleration. Therefore, in the case of uniform velocity the acceleration will be zero.

**Q **16. An object moves 18 m in the first 3 seconds and 22 m in the next 3 seconds while it travels 14 m in the last 3 seconds. Calculate the average speed.

**Solution**

Given data: s_{1} = 18 m, t_{1} =3 s, s_{2} = 22 m, t_{2} =3 s, s_{3} = 14 m, t_{3} = 3 s, average speed =?

**Q **17. An object starting from rest undergoes an acceleration of 10 m/s^{2}. Find the distance travelled in 5 seconds.

**Solution**

Given: u = 0, t = 5 s, a = 10 m/s^{2} We know that

**Q **18. Distinguish between uniform velocity and variable velocity.

**Solution**

If a body travels equal distances in equal intervals of time along a particular direction, then the body is said to be moving with a uniform velocity. However, if a body travels unequal distances in a particular direction in equal intervals of time or it moves equal distances in equal intervals of time but its direction of motion does not remain same, then the velocity of the body is said to be variable (or non-uniform).

**Q **19. A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.

**Solution**

Here we have, Initial velocity, u = 0, Final velocity, v = 40km/h = 11.11m/s Time (t) = 10 minute = 60×10=600s Acceleration (a) =?

**Q **20. What is retardation? Write its formula. Given an example where it acts on a body.

**Solution**

Retardation is a decrease in acceleration. This means that retardation is the rate of decrease in velocity. A positive sign of the magnitude of acceleration shows increase in velocity and a negative sign shows decrease in velocity. Formula: Example: When brakes are applied to a moving bicycle, there is retardation in its motion.

**Q **21. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis?

**Solution**

When the slope of a speed time graph is a straight line parallel to the time axis, the object is moving with uniform speed.

**Q **22. Speed is a scalar quantity whereas velocity is a vector quantity. Thus, state one difference between the two quantities important for distinguishing between speed-time graphs and velocity-time graphs.

**Solution**

Speed cannot assume a negative value whereas velocity can.

**Q **23. An object moving in a certain direction with acceleration in the perpendicular direction. Is this situation possible? Give an example of such situation.

**Solution**

Yes, The above given condition is possible. e.g. When a stone tied to a string is whirled in a circular path, the acceleration acting on it is always at right angle to the direction of motion of stone.

**Q **24. A runner runs 1.0 km south, then 2.0 km east, then 1.0 km north, and then 2.0 km west to return to its starting point. This trip takes 50 minutes. What was the runner’s average speed, and what was the runner’s average velocity?

**Solution**

Average speed =Total distance / Total time Total distance = 1 + 2 + 1 + 2 = 6 km Time taken = 50minutes =50/60 hours=5/6 hours Average speed = (6km) / 50 minutes = (6 km) / (5 / 6)hours = 7.2 km/hour Displacement is zero, because the runner returns back to its starting point. Total displacement = 0 Therefore average velocity = 0

**Q **25. Is it possible that displacement is zero but not the distance? Justify your answer.

**Solution**

Yes. If a body is moving on a circular path, then in one complete revolution the displacement is zero but distance is equal to circumference of the circle.

**Q **26. A motor boat starting from rest on a lake accelerates in a straight line at a constant rate of 6m/s^{2} for 6 s. How far does the boat travel during this time?

**Solution**

Given, initial velocity u = 0. Acceleration a = 6 m/s^{2} Time taken t = 6 s. Using the second equation of motion, we get S = ut + ½ at^{2 }S = 0 + ½ x 6 x 6^{2} = 108 m

**Q **27. Can the distance-time graph of a moving body be a straight line perpendicular to time axis? If not, why?

**Solution**

The distance-time graph of a moving body as straight line perpendicular to time axis is not possible as it represents different values of distance travelled at a particular time which is not possible.

**Q **28. Is the distance covered by a body always greater than the magnitude of the displacement?

**Solution**

If the body is not moving in a straight line, then the distance is always greater than the magnitude of the displacement. If the body is moving in a straioght line, then the distance is equal to the magnitude of displacement.

**Q **29. In a velocity-time graph, what does the area enclosed by the velocity-time curve and the time axis represents?

**Solution**

The area enclosed by the velocity-time curve and the time axis represents the distance travelled by the body.

**Q **30. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

**Solution**

When the slope of distance-time graph is a straight line parallel to time axis, the object is at the same position as the time passes. That means the object is at rest.