Chapter 4 Solutions — Describing Motion Around Us

Revise, Reflect, Refine

1. 1.
   My father went to a shop from home which is located at a distance of 250 m on a straight road. On reaching there, he discovered that he forgot to carry a cloth bag. He came home to take it, went to the shop again, bought provisions and came back home. How much was the total distance travelled by him? What was his displacement from home?
2. 2.
   A student runs from the ground floor to the fourth floor of a school building to collect a book and then comes down to their classroom on the second floor. If the height of each floor is 3 m, find:

   • (i) the total vertical distance travelled, and
   • (ii) their displacement from the starting point.
3. 3.
   A girl is riding her scooter and finds that its speedometer reading is constant. Is it possible for her scooter to be accelerating and if so, how?
4. 4.
   A car starts from rest and its velocity reaches 24 m s⁻¹ in 6 s. Find the average acceleration and the distance travelled in 6 s.
5. 5.
   A motorbike moving with initial velocity 28 m s⁻¹ and constant acceleration stops after travelling 98 m. Find the acceleration of the motorbike and the time taken to come to a stop.
6. 6.
   Fig. 4.27 shows a position-time graph of two objects A and B that are moving along the parallel tracks in the same direction. Do objects A and B ever have equal velocity? Justify your answer.
7. 7.
   A graph in Fig. 4.28 shows the change in position with time for two objects A and B moving in a straight line from 0 to 10 seconds. Choose the correct option(s):

   • (i) The average velocity of both over the 10 s time interval is equal since they have the same initial and final positions.
   • (ii) The average speeds of both over the 10 s time interval are equal since both cover equal distance in equal…
8. 8.
   A truck driver driving at the speed of 54 km h⁻¹ notices a road sign with a speed limit of 40 km h⁻¹ for trucks (Fig. 4.29). He slows down to 36 km h⁻¹ in 36 s. What was the distance travelled by him during this time? Assume the acceleration is uniform while slowing down.
9. 9.
   A car starts from rest and accelerates uniformly to 20 m s⁻¹ in 5 seconds. It then travels at 20 m s⁻¹ for 10 seconds and finally applies the brake (with uniform acceleration) to stop in 6 seconds. Find the total distance travelled.
10. 10.
    A bus is travelling at 36 km h⁻¹ when the driver sees an obstacle 30 m ahead. The driver takes 0.5 seconds to react before pressing the brake. Once the brake is applied, the velocity of the bus reduces with constant deceleration of 2.5 m s⁻². Will the bus be able to stop before reaching the obstacle?
11. 11.
    A student said, 'The Earth moves around the Sun'. In this context, discuss whether an object kept on the Earth can be considered to be at rest.
12. 12.
    The velocity-time graph from 0 s to 120 s for a cyclist is shown in Fig. 4.30. Shade the areas (in different colours) representing the displacement of the cyclist:

    • (i) while the cyclist is moving with constant velocity, and
    • (ii) when the velocity of the cyclist is decreasing. Also, calculate the displacement and average acceleration in the 120 s time interval.
13. 13.
    A girl is preparing for her first marathon by running on a straight road. She uses a smartwatch to calculate her running speed at different intervals. The graph (Fig. 4.31) depicts her velocity versus time. Estimate the distance she ran based on the graph.
14. 14.
    On entering a state highway, a car continues to move with a constant velocity of 6 m s⁻¹ for 2 minutes and then accelerates with a constant acceleration of 1 m s⁻² for 6 seconds. Find the displacement of the car on the state highway in the 2 min 6 s time interval by drawing a velocity-time graph for its motion.
15. 15.
    Two cars A and B start moving with a constant acceleration from rest, in a straight line. Car A attains a velocity of 5 m s⁻¹ in 5 s. Car B attains a velocity of 3 m s⁻¹ in 10 s. Using the graph, calculate the displacement in the two time intervals mentioned. (Hint: Calculate the acceleration in both cases. Then calculate their velocities at five instants of time to plot the graph.)
16. 16.
    Rohan studies science from 6 PM to 7:30 PM at home. Consider the tip of the minute hand is 7 cm from the centre of the clock (Fig. 4.32). During the given time interval, what is:

    • (i) distance travelled,
    • (ii) displacement,
    • (iii) speed, and
    • (iv) velocity.